For example, let's say a character wants to retrain a feat, it will take him 7 days (a week) of downtime.
Do these 7 days have to be consecutive, or can they be split? For example, could he retrain for 3 days, then go adventuring for 2 days, and then finish the last 4 days of retraining?
The craft activity does specify that:
If the downtime days you spend are interrupted, you can return to finish the item later, continuing where you left off.
But I'm guessing this only applies to that activity.
Further, there's this tidbit of rules from exploration and downtime activities:
If an activity that occurs outside of an encounter is interrupted or disrupted, as described in Disrupting Actions below, you usually lose the time you put in, but no additional time beyond that.
But I'm not sure if this refers only to disruptions, or to any interruption.