Chosen Solution

So, I bought each of my kids a refurbished iPad 2 a couple years ago for games and learning activities. The wi-fi on one of them inexplicably stopped working after about a year. If I turn it off and on or do a hard reboot it will work temporarily but then disappear altogether again. Upon startup it will recognize the local network and allow me to log into it, then within a minute it disappears and doesn’t even detect signals anymore. It also seems to lockup on the wi-fi screen in settings making it difficult to quickly turn the wi-fi off and on for troubleshooting. Is this a hardware or software issue?

It sounds like a software issue. I would do a factory reset and see if that fixes it. If not, the wifi antennas on iPad 2s are pretty famous for sucking. Its basically a little sticker to the right of the home button. So a well placed drop or a little spilled liquid can take it out. Do a factory reset, restore in itunes. See if that works. It should. If not: iPad 2 Wi-Fi EMC 2415 Bluetooth/Wi-Fi Antenna Replacement