I have 4 mapped drives to a "SimpleShare" network storage device. 2 have no passwords and 2 have passwords. On Windows 7 Pro PCs, Randomly, 1 of the password protected drives loses connection. The dropped drive changes on different PCs.
Windows has a idle timeout for mapped drive connections; by default it's 15 minutes. This may be what you're running into.
The non-password protected drives reconnect as soon as you try to use them again (without asking for a password) so you probably don't notice they're doing it as well.
You can see how long your idle timeout is set to by opening a command prompt and typing:
You can set the timeout limit (in minutes) as such:
You can turn off the idle timeout completely by entering:
See this MS article for more info.
Hope that helps...