Well I'm sure glad the APr works in FS2000! The one in Fs98 SUCKS, BAD!!!
I do have FS2000, and I play it every once in a while, but my computer has issues and usually crashes before I get anywhere in FS2000. This is why I'm still using FS98 religiously.
Soon I'll get upgraded and give the new APR a whirl!!
OK, back to the topic! I know many reasons why your plane might have gone off the runway, I've had the same problem before!
First, before you land, make sure you turn numlock off and then hit keypad 5, that'll center your rudder and nosewheel.
another problem could be wind. Go into the World/Weather/Winds area and check ground level winds before you land. If it's anything above 20 kts, you'll have a problem. Set it lower, or perfect your skills!
Another problem could be uneven reverse thrust. If you're throttles aren't locked, the pull will be great on one side and nill on the other, spinning your aircrft off the runway. Make sure the throttles are linked.
Make sure the second your wheels touch the ground that the autopilot is off!! Especially the autothrottle! sometimes it'll make #1 engine spool up to full while #2 is in idle!!
Anything else? Can;t think of any othe causes right now.