What's the difference between the Completed and Sent status?
Completed: the message has been forwarded to the network
Sent: the message has been delivered to the handset (or network if handset delivery notifications aren't supported).
If messages are stuck on Completed, it means we haven't received a delivery report from the networks yet. It's more than likely that the message was delivered to the handset, since if it failed, we definitely would've received a failure report.