My IPhone 5s has no problem connecting with wifi with Pokemon go. Whenever I try to get off wifi the app says no connection. So I go to settings and try to use data on the app and it doesn't appear in the cellular list. My provider is AT&T. I also use LTE
Are you out of data? Unless you have unlimited data plan, or an autobill re-up for more data, you're probably out. Ask the person who manages the bill to check for you.