My new iPad drops the wifi and reports that the password is wrong

Since I first set up this iPad around 3 weeks ago I've had this problem. Set up was without transfers or extra apps, so the iPad is clean. Fixes I've tried are rebooting my router, doing hard reboots of the iPad, and resetting the network settings on the iPad. Apple has done remote software and hardware checks and say there are no faults. I tried the iPad on a neighbour's wifi - same problem. Finally yesterday I reinstalled the OS. All of theses actions make the iPad wifi work but for a short time only. Does anyone have experience of this? And solutions. Thanks.