the .ldb is autocreated by Access when an Access DB is opened. Sounds like the Access DB is not being closed upon completion of the DTS package.
I would check the SQL server and see if the Access DB is open the next time this happens and end task on Access and see what happens (last resort).
Try adding the below into an ActiveX step as the last thing your DTS package calls:
Function Main()
Main = DTSTaskExecResult_Success
End Function
This may help close the connection....