Bernhard,
You might try stopping/disabling the Blackberry Database Consistency service. I cannot scientifically say yet that it's the answer to all my problems (I had very similar ones to yours, but so much was going on it was hard to pinpoint the real problem), but I do know that when I reinstalled all components freshly Jan. 5th, starting off with the BB Database Consistency service disabled, I've been running so smoothly with our two test Blackberries. That's ten days straight, something I never achieved in my previous setup that, as far as I know, only differed from this setup with that service being disabled. Might it have just been the reinstall? Sure, it could be, but I'm wary of turning on that service now. I could not figure out before how to get the Agent service to run stably, and we quickly reached the maximum of 10 restarts in about 10 minutes, well under 24 hours!
By the way, I got the idea to try disabling that service at all from this forum:
BES Problems.... The description of what the service does sure sounds like it would be important, but this Zimbra employee said it is not. Perhaps unrelated to your problem, but easy to try.
I'm on 5.0.10 Network Edition 64-bit SuSE Enterprise server 10. And BlackBerry Enterprise Server Version: 4.1.6.10 (server configuration tab in BB Manager). ZCB used was ZimbraBESConnector-5.0.10_GA_2514_5.0.2676.10.msi.