Windows

When you mapped the drives for the first time did you put the check in the box to map the drive the next time you logged in?

If you want to map from the Explorer in the 'Map Network Drive' dialog box you have to check the checkbox 'Reconnect at Logon'.
Second way is to type something like this in command prompt :
net use m: \\server\my_drive /persistent:yes

I had something similar, but on a novell network witn NT4 clients. Turned out it was bad cables that lost connectivity and the user ended up getting logged out and lost thier network mappings. For the laptops, check screensavers and power/sleep modes to make sure they aren't messing up the network connectivity.

Make sure you have good connections to the network, that can cause them to disappear.

go with propoesed answer 1 and 2