Maybe you can try something like the following so they get a fresh mapping every morning. Unless when you say "It seems to happen around the time of a lease renewal" you mean more than once a day.

code:
If Exist ("H:\*.*")
   USE "H:" /DELETE 
Endif
If Exist ("S:\*.*")
   USE "S:" /DELETE 
Endif
USE H: "\\Server Name\USERS\"
USE S: "\\Serer Name\SHARED"