Maza 3 2011 - power steering takes anywhere from 5s to an hour to engage

We have problems with the power steering on our Mazda 3 2011. After starting the car up it can take anywhere from a few seconds to an hour for the power steering to kick in. During that time the power steering warning light is on and it’s extremely hard to turn the steering wheel – as expected. We have owned the car for several years and most of the time it takes just a few seconds for the power steering to engage but sometimes there are weeks or months when it takes minutes or up to an hour of driving/being started up for it to engage.

We took the car to Mazda service a few times to get it diagnosed but by the time we got there the power steering was working and they didn’t find any problem.
We tried replacing the battery too and didn’t observe any noticeable difference.

One more thing to note is that if that once the power steering engages it continues to work flawlessly until you park the car for a few hours. If you just park, go shopping and come back to it it engages fast. But if you let the car sit overnight, the problem is back. That is the only pattern we noticed.

We’ll be trying some smaller car shops close by in the hopes that we can get there before the power steering engages and they can diagnose it, but any ideas?

Thank you,
Tereza.