Is the person making the call on the 6961 muting themselves? J/K unless your taking someone else's word and not checking for yourself. Then the first thing I would do is check for yourself.
Is it happening with multiple 6961 phones or just one?
If the phones are in the same subnet and you can rule out a routing issue, then I would search
the bug search tool for the specific issue you are facing.
https://tools.cisco.com/bugsearch/
If you strict out I would still check for updated firmware
Which you are little behind on since cmterm-69xx-sip.9-4-1-3.zip is out.
You can read the release notes for your current firmware and the updated firmware if you want to try to find the issue, but I believe now the release notes just points to the bug search tool.
Then I would Update the firmware to the most recent release for both phones types and then if you still have the issue and you have smartnet, call TAC to have them assist you the trace.
If you want to troubleshoot more on your check the codec that is being negotiated during the call by going into the both phones web pages and looking at the stream 1 field or whatever it is called. You can also see more information about the call here.
If you wanted to dive deeper into it set up SPAN on the ports the phones are attached to and run wireshark to look to see if you see anything weird.
