I have two domains that are successfully hosted by Google and have no problem using the Google app email in iPhone and iPad.
Another domain hosted on Google (early this year) has had constant problems in the Mail client on iOS. I have checked settings over and over and the account works and then dies. Sometimes coming back up for no reason. This has gone on for months.
I compared all the settings in Google App admin line for line, and they are the same in all accounts.
Could it be a DNS issue? The accounts that work both have the same A-record, the non working account has one that ends in a different number.
It seems plenty of people have this problem - there are long threads on the net - I have tried all the suggestions.