This morning I decided to just turn off wifi for a few minutes and then turn it back on without messing with cellular data. Before turning wifi off I was having no issues with wifi dropping out. After turning it off and then back on a few minutes later it began to drop out when sleeping.
So I guess the problem isn't related to cellular data at all but is related to turning wifi off and on. FWIW, I use widgetsoid in the notification menu to turn it off and on. Not sure if that has anything to do with it or not.