My new tubeless tyres wont stay inflated

A reputable bike shop that did work on your bike with unsatisfactory results should make every effort to make it right at no additional cost to you. If you have a receipt documenting the service and amount you paid, bring that and the bike along with you. Even if it's been a bit of time (a couple weeks to a month), it's perfectly legitimate to bring the situation to them and expect them to fix it. Management--as well as a quality mechanic--would want to know (and correct) any problems resulting from their work. It may be a situation where some product isn't working as expected, or perhaps a new mechanic needs more or different training. In any case, they need to be aware a problem exists in order to correct anything, and that's where you come in.

This is what I've taught my children: when you purchased a product or service and that product is defective or the service incomplete or done poorly, you should make the store or responsible person aware of the defect or your disappointment in a polite and clearly stated summary of the problem. Conclude the summary with a sentence or two that definitively states your expectations. No one can meet your expectations if they are unaware of what they are. Having in your possession a receipt or other documentation that outlines the work performed helps to bolster the legitimacy of your claim, although absence of such things is not a reason to not stick up for yourself. In your case, the question you've posed to Bicycle Stack Exchange would be alright at the bike shop. Add to it a sentence or two stating your expectations.

The advice in the comments above--especially trying to find where it's leaking with soap and water solution-- would be something you could do to show you've made some effort to help find the problem. Marking any areas where you've noted air bubbles (using something impermanent like tape or chalk--just nothing that would mar the product in case they choose to take them back). Should an employee of the shop refuse or in any way impede your expectations, politely request to visit with a manager on duty and again restate to him or her the clearly defined problem and your expectations.

Here are the likely reasons:

• You don't mention timeframe between inflations. Even when things are right, tubeless needs reinflation fairly frequently. It's approximately akin to an ultralight tube. Making it through a ride shoudn't be a problem, and it shouldn't just lose all its air unless sitting for months, but it will lose a meaningful amount of air in the 3-4 day timeframe.
• You also don't mention timeframe since initial setup. How long the sealant is good for varies, but needing to refresh it after 3-6 months is normal.
• The amount of sealant might not be enough. This is one of the trickier parts of doing a tubeless setup as a shop mechanic. Tires vary some in how much sealant their sidewalls eat before you have a desired target amount of free liquid sealant. Sealant manufacturers don't really account for this in their setup instructions because they want simplicity. You then have a guessing game to play as a mechanic where you're trying to give it enough without making it too heavy. When the instructions say 2-3oz for the tire size you're doing, it can feel like you're doing something wrong when you add an extra 2, but that's exactly what I've had to do sometimes to get past the threshold where there's any free sealant to speak of. The supple gravel/allroad tires are where this can easily come up. This issue, and the above issue related to the sealant getting depleted over time, can show with a soap test as air bubbles making it through the tire casing, including random spots on the tread/sidewalls or previous puncture spots.
• The tape job could be bad. Also totally possible, and not less probable by virtue of the issue happening on both. If it's losing pressure immediately or not taking pressure at all, this is the most likely. The above issues will still allow it to pressurize. This will show with a soap test as leaks through any or all the places the tape is supposed to seal, i.e. anywhere but the tire casing.

Sloshing the sealant around to distribute it is necessary in a shop because if you don't, air will leak through the casing and so you won't know if failure to hold pressure was caused by that or by other issues, such as tape. And in some cases it's necessary to make it seal at all. But if you've riden the bike, that will distribute it as well as anything, so it's not likely that failure to slosh is the actual cause.

I will repeat and expand on the points from my original comment even if I generally detest answering questions where more information should be supplied first and call for waiting for that information

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Firstly, if you let the shop to prepare the tubeless setup for you bring it back to the shop.

How long should a tubeless tyre stay inflated - be prepared to pump it every few days by several PSI even in a well-sealed tyre. Some air will always escape somehow and more than with a butyl innertube. But it should not get to a half of the original pressure overnight, that is a clear sign of a big problem.

There are many things that could go wrong and cannot be identified from your very insufficient description. To repair something, you have to know what is wrong. That is best achieved by identifying the location and the nature of the leak.

Air exiting from the place of contact of the tyre with the rim - wrong seal. The tyres are not seated properly or may even be not compatible enough with your rim. Let the shop to try to seat them better. More sealant could help - or not.

Air exiting around the valve: incorrect valve mount. The valve/rim interface is not tight enough. Sometimes tightening the nut helps. Sometimes it must be re-installed or the tape must be re-installed.

Air exiting around the spokes: incorrect tape installation. If the tape is not installed properly or is torn, it must be reinstalled.

Air exiting through a hole in the tyre: a puncture. More sealant could plug it. If it is big, other ways how fix holes in the tyres are described in other questions and answers.

Air exiting through the tyre material at many spots: wrong tyre, most likely not tubeless-compatible or damaged by improper handling, use at extremely low pressures,...

Overall, wrong sealant or not enough sealant is the least likely cause, once the seal is achieved, the tyres can be run totally dry for weeks - if one does not puncture.

The location of the air leak can be identified by listening to any hissing, watching for sealant making bubbles, submerging the tyre and looking for air bubbles or by wetting the tyre with (optionally soapy) water.

Let's repeat the main point: Bring it back to the shop if they prepared the tubeless setup for you..

Tubeless tires are a performance modification, for lower rolling resistance, traction, and...in certain forms, but by no means universally...lower weight. In some types of terrain and riding, tubeless tires may be required to prevent constant flat tires. However, these performance advantages generally come at the cost of convenience and maintenance. Tubeless tires are not a "convenience" modification.

It is relatively normal to have to air up bike tires before every ride. There is a reason that classic road bikes had attachment points for a frame pump...tires need pumped up; it's an unfortunate fact. For some commuting and city riding applications, where this is inconvenient, it is best to stick with inner tubes...and thick inner tubes at that.

It's possible to achieve a tubeless setup which is similarly air-tight...but it's work to get there. Work and money that may be better avoided by simply running tubes, if you can do so without flat tires being too frequent.

The best such tubeless setup that I have found is to use a thick, heavy tire (in my case, Maxxis Hookworm 2.5), set it up with a full-width latex rim strip (like FattyStripper or equivalant) to completely seal the rim and beads, and use a generous amount of sealant (Stan's). Using this setup on my cargo bike, I can go a month or more before pressure drops from 35 PSI to 25PSI or so requiring me to add more. It was similar when I ran tubes, but with the tubeless tires I also avoid punctures. Most of my other tubeless MTB tires require pumping up every ride. Most of the leakage is probably at the beads or through the tire itself.