I do notice QC has a timeout of 0.01 for auto caching but i assume your pages are caching partially the normal way (by visiting the page and it caching in real-time). Its real-time cacher (non-auto-cache) doesnt have nor need a timeout setting so its intriguing your problem.
How slow is your site?
Have you tried disabling other plugins to make sure its not some plugin conflicts?
I'm looking over the QC code and right now i do see a situation where the buffer can timeout and it will just dump out what it has (hence: partial). But the situation seems to indicate your server is really bogged down and just giving up part way.
Curious..at the bottom of your "partial" cache file does it show the standard: <!-- This Quick Cache file was built for or is it missing?
Btw, check for the error_log file for more info.
You may want to turn on WP_DEBUG in your config file too.