You are using hardphones, and you tried moving them to a DMZ so as to rule out the NAT firewall from the picture (ie. phones and the Axon server are both directly accessible from the Net with no NAT in between), but calls still fail at some point. So I would guess that Axon is the culprit.
FWIW, here's what I observe using 1.09:
- sometimes, clients that are located behind a NAT can no longer register to Axon accross the Net
- sometimes, Axon no longer reports incoming calls that are routed by a Linksys SIP gateway.
In both cases, restarting Axon solves the issue. That doesn't definitely confirm that Axon has a bug there, but as a test, you could restart Axon every hour or so, and see if calls no longer go quiet.