My external HDs drop off "my computer"?

I have a brand new Windows XP Media Center Core 2 Duo HP computer.

From my old computer I took my internal hard drive (with all my photos on it) and put it in a USB 2.0 enclosure so now it acts just like an external HD (called "K" drive now). I also have a second external HD with digital video on it (called "L" drive).

I have had this happen at least twice: I am working in my photo software (has happened in more than one piece of software) and all of the sudden my K drive is no longer recognized by my computer. The hard drive is on but it does not show up in "my computer." Same with the L drive; it is just not recognized by my computer. As soon as I reboot, both of them show back up in "my computer."

Can anyone tell me what is wrong? Is this just something I have to live with?

I really appreciate your help. I am not a high level computer person, so if you can help, much appreciated!