Time Machine fails most of the time on one Mac

I am having the exact same problem with my ReadyNAS Ultra 6 on an early 2011 MacBook Pro. If I unmount the ReadyNAS volume, that usually works--until a few hours or days later, when the problem starts all over again. Sometimes I have to use the umount command in Terminal to unmount the disk. I also did not have this problem before Lion. (My wife's early 2011 MBP is still using Snow Leopard, and never has this problem.) So, why won't OS X Lion unmount? A possible(?) clue is that before Lion, I was also able to use TM to backup to a USB disk on Airport Extreme. Yes, I know it wasn't supported, but it would work more often than not. Now, that never works--TM won't even see the disk.