As others have said, a month to 6 weeks was a typical patrol duration until boats started going long haul to try and find more targets. However, don't feel you should force yourself to stay out this long unless you're deliberately trying to go for authenticity. With a bit of recklessness, a lot of luck and a severe case of throat itch you can be done in a fraction of the time.
I've always patrolled until I'm either out of eels or badly damaged; I've had some phenomenal luck finding juicy targets in my current career and will pursue targets relentlessly. My patrols have been completely ahistorical in terms of their duration:
-Shortest patrol is 7 days, returning due to a botched harbour raid getting my sub smashed up pretty bad.
- Longest patrol is a mere 20 days, returning empty after interdicting two different patrols off the west coast of Ireland.
I have spent only 126 days at sea in 9 patrols for 470115 tons sunk between 01/09/39 and 17/10/40.
Obviously this makes a mockery of the real statistics, but it sure makes for a fine game
