The last I heard, BES for GroupWise is supported only with the NetWare/NLM-based version of GroupWise. I've heard rumors that others have gotten it to work with the Windows vesion of GroupWise, but kudos to BlackBerry for working with you when it's not running in an officially supported platform!
Is the entire server locking up, or just the MTA process? What logging level are you using on GW and BES? Both can be set to "debug" level which might provide a better idea about what's happening.
Before you start digging through reams of logs though, have you done any database maintenance on the GW system? At a minimum, validate the domain and post office databases.
The other thing to try is to shut down BES for a while to see if the GW server still has problems. My understanding is that the BES server appears to GroupWise as just another GroupWise client. So if there's a problem on the GW server it may be just a coincidence that it started a few days after BES went live.