I'm fairly certain this is not normal behavior, even on a Verizon iPad. Unfortunately I can't think of anything that could be causing it.
If the iPad hasn't been restarted recently, that is worth a try, but I wouldn't put any money on it.
Hold down the On/Off button until the red power off slider appears, and slide it off. After the iPad finishes shutting down, wait a few seconds, then hold the On/Off button down again until the Apple logo appears.
You could also try going to Settings >> General >> Reset, and choose Reset Network Settings. You'll have to manually join your home network again, but it might work better a second time around.