Messages stuck in Outbox

For the past two days messages we wish to send are getting stuck in the Outbox for up to a few hours. We went to 2 AT&T stores getting different answers (old phone) 5S and 5C and changing reset etc. to no avail. Sent to Apple Store set up a phone appointment for 8:30pm, never called until 11:30pm (missed call). This am seems ok for now. It happened on 2 phones. What is going on? HELP!!!!!!!!!!!!!!!!!!!