Hi- I doubt it is an issue with CTI messaging. You'd have to turn on Meridian Link trace messaging in CCMS to determine what is being sent from the PBX across the CTI link. You'll most likely you'll need your vendor to turn these traces on and decipher if you get to that point.
I work more on the CCMS/PBX side, but we had this exact problem using NICE. We are not yet on version 3.1 (still on 9x), but I believe NICE SP4 resolved our problem.
If the "ring-in" link message is getting to NICE most likely the "end call" event is making it.
Good luck.