Does anything show up as an error in Device Manager (yellow exclamation mark)? Are all the drivers the correct ones for your o/s and updated?
You didn't say what o/s you are using, but if you have Win2K or XP, you could look at Event Viewer
(Programs/Administrative Tools) and see if any errors in the logs correspond with the problems occurring.
Might sound too obvious, but have you looked into possible physical hardware causes? Is this a new PC, or one you have built/modified yourself? Is it a recent problem, ie has the PC run for some period of time with both drives OK?
Possible h/w problems I would look at - loose/bad ribbons, power supply (check voltages when the drives disappear), jumper settings esp. if they share a ribbon (Master/Slave/CS). How about IRQ conflicts - run System Information from the System Tools menu. Anything odd in the BIOS? The mouse locking up could just be as a result of the O/S having to deal with the stalled drives.
Are you running any programs when this happens, or accessing media in the drives?
Odd problems like this usually require a process of elimination to track down. Try uninstalling/removing one of the drives and see if the other one behaves.