It sounds like you have a hardware detect configuration problem causing the disconnects. This is usually set in class 4 and 5 switches with E&M signaling. This will ensure calls properly disconnect when someone hangs up the phone (reversal ground, I think). Typically this is set with a timer to disconnect if caller/switch/PBX doesnt send the hardware off hook/on hook signal (ground reversal?). Most switches can be set to detect hardware answer- off.
Make sure the switch is sending back a connect. If we don't get a connect after 3 minutes (if memory serves me correctly) we'll disconnect the call. If you can't find anything, go ahead and open up a TAC case; you'll need 'show ver', 'show run', 'debug voip ccapi' and 'debug vtsp all' OR 'debug vpm all' depending on the platform/version.
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...