One way audio problems can most of the time be traced to NAT (I agree with what you suspect). The loss of inbound RTP (audio) sometime after the call started might indicate the router (performing NAT) has closed the RTP port.

Can you try to correlate the time before the loss of audio happens with one the NAT router timeout settings ? If you can find a match, it would help to get a little closer to the source of the problem.

Regards,
Norm