I've been unable to successfully suspend and resume Fedora Core 6 since I stopped using build 1970 (this includes the past two betas before 3106). The suspend completes successfully but upon resume the screen is corrupted and the VM is unresponsive.
I've had the unresponsive problem with Build 1970 and also with VMWare. So, I don't think that's Parallels fault. However, I haven't seen a corrupted screen; that part may be new with 3106. I'm not running 3106 or any beta yet. I don't run beta's in production environments unless there's no alternative (i.e., VMWare for 64-bit).
I've actually just experienced the hang when using pause as well. I paused my VM, closed the lid to sleep the mac for the night, then when I tried to unpause this morning the VM was unresponsive again.