it was common practise with the Bt wholesale ISP's due to the fact BT wholesale changed their pricing a few years ago
it was called UBC and CBC
usage based charging and capacity based charging
UBC meant a small start up cost for the virtual circuit but BT would charge the ISP a certain amount based on that Virtual circuit' usage in terms of downloading etc, the ISP would then pass on that charge plus a bit extra [profit margin] to the customer, hence why you saw free setup and cheap monthly access with bandwidth caps 🙂
CBC was based on the size of the virtual circuits they would rent off BT wholesale, so higher start up costs and higher monthly rental with little or no bandwidth caps
so how does this relate to your drop outs, well BT wholesale ISP's use to reset their central pipes in the early hours of the morning daily to reduce bandwidth use and connections thus saving themselves money as the end user would hardly be awake and their downloads would be reset or simply stop until the user prompted them to start up again
in your T&C's it will not cover these drop outs and your SLA will not cover this, if you want 24/7 constant access then buy a leased line or business adsl connection 🙂
Bethere does not use Bt core networks nor does it rent a central pipes, it has it's own central pipes as they are run by a company called telefonica, O2 now use the same pipes as bethere so effectivly i have the same connection as a bethere customer but for less money 🙂