You could try to back up your iPad, factory erase and then restore from the backup just to see if it might work...It could very well be a hardware issue as scifan57 had mentioned.
I called Apple. She tried to help but needed to call me back several days later. No call back. I discovered when I had the ipad closer to the router, I had no problem. Ipad recognized my home network and connected, as usual. I called my Internet provider and haven't had the problem since then.
I'm also having trouble with ipad2 staying connected to wifi. I don't know too much about all this. I did take my router to have it checked and reset or whatever and they said its fine. Believe they changed a channel. I also called my internet provider and the speed is fine also. Could it be the age of my ipad2...its about 4 years old. I also am unable to stream Netflix through the ipad to my TV anymore. Any help appreciated.
You could try forgetting the network (from your WiFi settings), turning the iPad completely off for a few minutes, then rejoining. You shouldn't have a problem connecting an iPad2.
Try what Jupiter7 suggested again, but this time turn the router off for a minute or two, while the iPad is still off. This resets the connection on both devices, and has been known to work when reseting just the router or iPad does not work.
And no, it doesn’t matter that other devices/computers are working fine. Each devcie has it’s own connection/record with the router, and can misbehave without affecting the other devices.