It is more then likely a internet communication issue thats causing the users to drop out.
Ive been setting up a few clients recently who are expanding into remote offices and have installed 4 x Bonded ADSL lines into the head office to handle the extra critical traffic that needs access to the server. It also means if one of the lines has a problem the other 3 are still active keeping them online.
Bonded ADSL works out a lot cheaper then SDSL lines or Leased Lines.
I would strongly recommend looking into your connectivity options at the main office and looking for ways to expand the incoming capacity / reliability.