As well as RHP I also play at gameknot.com. There they have a system by which the timed out player can ask their opponent to continue the game from the point where the timeout occurs.
The opponent has the choice of whether to accpet or not and whichever the case, the initial result (defeat by timeout) always stands. Effectively you would be starting a new game from the old board position.
You are only allowed to do this once per game, and not at all (obviously) during tournament games.
Gameknot also has a system which allows you to actually postpone your games if you go on vacation, but has a limit to the number of vacation days per year to prevent abuse. There is also a limit to the way these days can be used up i.e. if you postpone for ten days, you are then not allow to postpone again until a further ten days have elapsed.