Heavy Rain not only seizing up but (in a few cases) corrupting their save data; you can read all the stories on the PlayStation forums. Info is limited at the moment, but a Sony rep in the thread suggested the stopgap of waiting at least five minutes before rebooting if a freeze occurs. The rep seemed hopeful that measure would enough to avoid save data corruption.
Heavy Rain is intense enough without having to worry about losing your save data at any moment. Here's hoping we have word of a fix soon.
[Thanks, Ryan S.]