Hello, Barney.
First thing, if you're running CallManager 3.3(3), is to make sure you are running the latest service release. That is SR4A as of this writing. The initial SR4 release had a very critical bug which caused route points and route patterns to occasionally disappear out of the route plan. We have worked together in the past on a customer in Rosemont, IL who I know was running SR4; if this is about them, you should upgrade them ASAP.
After that, you need to narrow it down to a TCD issue or a gateway/codec/location issue. Take some number of phones in the same Region and Location as the TCD hunt group, and fill up the TCD hunt group repeatedly until you spill over into voicemail, preferably multiple calls into voicemail simultaneously.
If you can't get through an internal test successfully, your problem domain has been reduced to something wrong with TCD and you'll want to work with Cisco TAC. If that test does work, you probably have a problem with a gateway CSS, codec/region or location. You're having trouble finding the voicemail pilot partition, or you're having trouble getting a transcoder in the loop for a g729 call into the g711 Unity system, or you're out of location call admission control bandwidth.
-jyoung
