Mike-
I shot next to you this weekend (both during the AP match and the FP match afterward). This was my 4th-ever air pistol match (the first three were in 2009, 2010, and 2011 at the NRA Open International Air Pistol Sectional match at the Rockville IWLA until Tom W. stepped down and no one else wanted the job of running the AP matches), so I can only tell you how I trained/practiced leading up to it:
I shoot a lot of NRA Conventional Pistol, and I shoot it pretty decently (at least in .22). On the Wednesday, Thursday, and Friday before the AP match on Sunday, my range sessions were:
1. A National Match Course (10 slow, 10 timed, 10 rapid; full distances and timings) with my red-dot'ed Bullseye gun to warm up, to start on a good note, and to get a feel for how I'm shooting that day. If I'm not doing well with my 'normal' pistol, I don't think I'll be any better (and may be a bit worse) when I shoot my iron-sight pistols.
2. A National Match Course with my iron-sight'ed Sport Pistol, again diagnosing any issues I might have with that kind of gun and sighting system.
3. 30 rounds through the freepistol.
4. And finally, 30 shots through the air pistol to rebuild my self confidence. Keith Sanderson
quoted one of his shooting teammates as saying "Air pistol: it's like you are a general, and the pistol is a private, and you tell it what to do." Spending those last 30 shots with the air pistol helps me recover from the humbling experience of trying to shoot the freepistol (Sanderson also quoted his teammate as saying: "Freepistol: it's like you are a general, and [the pistol] is a general, and you negotiate!").
To build on what
rmca said: while I only shot 30 shots through my air pistol in my above practice routine, those 30 shots come after 90 shots through other guns, 50 of which are in the same style (slow fire). So I'm effectively practicing for a full 60 shots + sighters match - an hour or more shooting nothing but one-handed slowfire.
I also shoot air pistol last in my routine because I shoot on a public range (the NRA HQ Range in Fairfax, VA) and I'm only guaranteed an hour of uninterrupted time; if there's a wait going for my lane, I'll probably be kicked off. If I get kicked off, I can always go home (I live nearby) and shoot air pistol in my house.
I did not shoot on Saturday both because I was out of town the entire day for a wedding, and because I needed a break from shooting - rest is important too.
When the range is closed to public shooting (Tuesdays), I have the option of shooting at home - and during the couple weeks leading up to my previous (third) AP match in 2011, I shot 20 shots about every other morning, and then shot my normal range routine in the evenings (back then I was more focused on NRA Conventional Pistol, so I basically just shot double-length National Match Courses with my .22 and centerfire pistols).
Mike - all of this is basically saying: I put a lot of time into practicing/training for the relatively long matches (I think of AP and now FP matches as being 70-round slow fire matches, broken up every 5-15 minutes by the need to change targets). This only addresses the stamina part of it, though.