This is an issue I brought up in the past but could never get it solved.
The problem is on any remote extensions, the connection is very unstable. Sometimes it will be perfectly fine, but more times than not, calls will cut off after about 30 seconds.
Have you read any of the forum posts that sound a bit like your problem?
Do you see how after pulling teeth for a few posts some get a clue and post all the diagnostics and trouble shooting they have done to fully describe their particular deployment and their particular problem, in the absense of any of that you will have to wait for a mind reader to show up, but unfortunately for you, there are very few of those around here
Yes, I don’t know how the Mitel’s do NAT if you have to manually configure the external IP. What is the remote network architecture? What kind of routers? Internet connection? What do the RTP logs look like when the call is dropped (if you are going to post them we only need 1 line, not 500 duplicates).
Many phones work poorly behind NAT. Mitel’s are not widely used with Asterisk (compared to other vendors). You could avoid all the trouble and setup VPN’s to the remote site $25.00 routers have this capability today.