I also have the same problem.
I am running Windows 7 64 bit on a new VAIO z series laptop, and hibernate fails (leaving the machine running with a blank screen).
It is definitely caused by ZAP.
I'd like to continue using ZAP but this problem is very annoying. I have often found my laptop running 'dead' like this in the morning meaning its been on all night (when plugged in), or until the battery runs out.