Samsung S4 constantly losing connection, but still shows connected.

My girlfriend's AT&T S4 loses connection, but still shows it connected. So you never know you don't have a connection until you reboot the phone and find that you have missed 2 phone calls, 3 emails, and 15 texts. This happened with the stock Rom. I've tried a couple of different roms, but still the same outcome. I'm thinking I should have to switch to a different modem, but I'm not sure which one to use. Am I wrong and is there another solution? I'm looking for something that will work so I don't have to mess with it again. If anyone has experienced this connection loss and found a solution, please let me know what to do to fix this phone.