I suspect that your computer is crashing because of a hardware problem. Lemme guess which one:
1. Overclocking CPU
2. Laptop
No. This is a dedicated computer which only runs a mining program and Bitcoin. It is not overclocked, it is not a laptop. It is a well ventilated desktop.
Bitcoin does not have any error message relating to disk space; when it runs out of space to download the blockchain it just crashes. Such an error would be from the operating system. Errors in the disk file allocation table may report incorrect free space to you or to applications.reboot when prompted.
Here is an exact error I received a few times:
EXCEPTION: 11DbException
Db::get: Not enough space
C:\Users\Owner\Desktop\Bitcoin\bitcoin.exe in AppInit()
Now when I load it, I get a "Runaway Exception" after it sits there for several hours not downloading any blocks.