What type of messages appear in the pix logs at the time of the disconnect? Does the link LED indicator(s) change color (say from green to amber or dark)?
Is your issue only with vpn connectivity or does it arise with non-vpn activity as well?
What device does the 501 unit connect to? There may be an issue with the switch or router unit.
One item to check is the pix interface config: If possible hard code the speed and duplex settings of all of its links, on the pix as well as the device it connects to.
The bad hardware possibility can't be ruled out yet, but the log messages and the link speed/duplex are worth checking out first.
Let me know what you find.