Not stringently. If your character intends to do something between adventures, you can email the Far Shores account and tell us what your character is doing. This may prove rewarding, or might lead to encounters being run specificly for you before the next adventure. The refs check the email account regularly and will do their best to get a response to you promptly.
There are a number of different things that can happen within the downtime period that a character my achieve through such things as the crafting skills. Such skills have time limits on how long it takes to craft a specific item, this is generally two weeks.
For further information consult the crafting section of the Players Guide.