It seems to me that there are two types of "downtime" in a "lifetime" game - there''s time spent not even playing the game (even the most dedicated gamer has to sleep a couple of times a week, and a lot of gamers have something that resembles a real life as well) when, OK, the player could theoretically leave the machine running the game (in the background probably) and hope he doesn''t miss anything too important (his character getting killed for example) and then there''s in-game down-time when the character is, for example, sleeping, eating, travelling long distances... For player downtime, you can pause the game world, keep game time tied to real time (meaning either keeping the program running 24/7 or having to cope with a large amount of simulation backlog when the program next loads - either way you still need to consider how to avoid the player missing something important) or keeping game and real time synchronised until the next event that requires player attention then pausing the game there.

For character downtime, you can subsume it into player downtime (which means the player has to schedule his real life around the game - or the game has to adapt to the player''s life), you can skip ahead (faster time rate or straight skip) as discussed by previous posters, or you can allow the player to perform administrative tasks (juggling inventory, long term planning, levelling up?) play mini-games (playing chess against the caravan master during a journey for example) and any other aspects of the game that would be harder to do in the middle of an action sequence.