Mapped Drives

I am still having problems with mapped drives. I have
mapped a drive on two identical laptops. One of the
laptops tries to reestablish the mapped drive connection
every time the machine is restarted. The other unit waits
to establish the connection until dial up networking has
established the connection. I tried selecting the Quick
Logon, and I still get an error message at restart
saying "unable to establish the connection". Any other
ideas would be appreciated