The battery in my Nikon D3400 dies after 50 shots. What shall I do?

The possible reasons for such behavior can be:

1. You preview the images you take too much. Using the LCD screen can exhaust the battery
2. You use too much live view. Again using LCD is not good for battery
3. Your lens have image stabilization and you half press the shutter too long.
4. You have defective battery

This is not right. I'd try Nikon again. Explain that you understand that the battery is a consumable that might not be good in a year, but that it is brand new. If that doesn't work, take it back to the store you bought it from. And if that doesn't work, open a dispute with your credit card company (on the grounds "they sold me a lemon and won't take responsibility").

In a comment, you add:

As far as going back to the store is concerned, I'm afraid that won't be possible since I'm going out of town tomorrow and won't be back for another four months.

... well, it's not like Nikon is going to magically fix this over the phone either. From a practical photographer's point of view, this has a bit of a lesson: always make sure you either have back-up gear, or plenty of time to get things working. You should at the very least contact the store and tell them the problem. If you are planning on taking the camera on the trip, I'd consider changing my plans and squeezing in a visit to the store today.

If you do want to use the camera and don't have time for anything, I'd suggest buying a second battery. For one thing, you want to have that anyway. It'll be something like $50 for a legitimate Nikon battery (recommended) or $15 for a third-party one (probably fine). There's a reasonable chance that the problem is just with the battery, so maybe this will make it work. If not, all I have is the sad lesson to plan ahead better next time.

Note that new Lithium rechargeables will typically need about 5 charge/use cycles before they show their full capacity, particularly if they have been some time on shelf. How much use they will then endure before deteriorating again depends on their quality: second-market batteries often have a shorter lifetime in terms of recharges. If yours is original, it should have a comparatively long one.

So for now I'd recommend to just grit your teeth, use your battery until it is empty, then recharge. And hope that after a few times of that, the problem will sort itself out for a longer time.