I'm running Debian 7. I'm not having any problems.
My wife is running Debian 7, she is having problems.
The only difference is that I've been running previous versions of Qt and already had the entire blockchain downloaded.
She, on the other hand, is running Qt for the first time and attempting to download the entire blockchain. It gives her errors and has recently started crashing at start up. She's only about 1/2 way through downloading the blockchain.
Verifying the blockchain can be very resource intensive. It is akin to running a burn test on your system. It stresses the CPU and hard disk. So I imagine the problem is with the hardware. Maybe the CPU is overheating? Install lm-sensors to check the cpu temp. It could also be that there are bad sectors on your wife's hard drive. Use badblocks to scan for that.
