My Nest X is a couple of years old and has always had two problems.
1 When I put new batteries in, it says battery is 'ok'. After only 4 months, it still says 'ok' but I start losing connectivity. Change the batteries an full connectivity again. There was no low battery warning.
2 If my router restarts, the only way to reconnect it is sometimes to restart the lock, mostly have to factory reset it. It rarely reconnects itsely. This may be connected with the batteries being low enough to affect connectivity but strong enough to show as ok.
I use top quality Duracells or Energiser
The Connect, lock, and Nest doorbell are all within 10 feet of each other with no obstructions bar a wooden door. The router is 20 feet from the Connect obstructed only by floorboards.
Whilst I'm here, whenever I have tried to answer the doorbell in the app I always get a spinning circle.
I have strong 200Mb internet
I apologize for my late response and thank you for all of your patience while waiting for a reply. I definitely understand how frustrating your situation must be, and I wanted to make sure that your concern was acknowledged. Do you still need help with this issue? I know that there's been a delay in response since you posted.