I think I've found the manual for your 3Com box :-
(Caution - PDF link)
On Page 46 it details the "Internet settings" screen. There is a box about 2/3 the way down that is marked "Idle time". If this has a number in it; then the router will disconnect after that many minutes. Just empty that box and put 0 in and this will reset so that it should no longer disconnect.
If it's not that; then it could be a problem with the line rather than the router
Best of luck