Eyebeam is an excellent programme and well supported, if it keeps crashing then you have further problems not related to that particular application. I would suggest you investigate your firewall setup and check the way you connect to the internet (ports open or stun set). Eyebeam produces a log file that may also give you some clues on what is happening.
You will also find some further resources on the eyebeam specific forum at
http://support.counterpath.com/viewforu ... adb61bb264
There are some mac specific updates and fixes(to 1.5.16.2, check the version you have now against this) that can be downloaded from the above.
Let us know how you get on