How can I stop losing mapped drive connections to SimpleShare NAS device from Windows 7?

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:

net config server

You can set the timeout limit (in minutes) as such:

net config server /autodisconnect:<#ofminutes>

You can turn off the idle timeout completely by entering:

net config server /autodisconnect:-1

See this MS article for more info.

Hope that helps...