Been pondering this idea for several days. Joseph Fitz-Patrick made 17 patrols (according to Blair) but I'm not sure how many of those were as skipper (not all of them, I'm sure). Also, a few skippers who had been relieved got second chances, so I'd hate to see a career irretrievably over after only 2 patrols (although I agree it would be realistic). So maybe factor in a chance for reinstatement if relieved for failure to acheive results.
I think the idea of limiting the number of patrols for a career to a realistic amount is entirely a good one, but my two cents would be to incorporate it via a mod rather than have it built into the stock game without any player control over it. I think the average or first-time player would not like to have limits.
Several skippers (thinking of Moon Chapple, one of the ones given a second chance) went through the war from start to finish, so if the number of patrols must be limited, IMO it'd be good to have them spread out - so you don't, for instance, start December 7 and find your career ended before Midway (unless you're dead, of course

).
[
Edit: Just thought of something else - Lockwood or Christie think it was Lockwood) nearly always "relieved" his skippers for a rest after they'd completed 5 patrols. Based on Blair's top 76, the average number of patrols completed was 5.2.]