You don't have to rip the tape off the exact second after you paint over it, but don't let it get super-tacky... when latex paint becomes super-tacky, it'll tear like paper... you may have seen this if you've ever pulled tape off of a recently painted door frame or baseboard - the tape will pull up on the paint that's bled through and the tackiness will then cause it to pull on the surrounding paint.
Obviously paint will run if it's slopped on to much - pulling the tape off will only give it a place to run. Since you're painting a "moveable" object, you could consider turning the painted area so that if paint is going to run, it's going to run in the opposite direction of the tape... does that make sense? If the tape has been put on properly, the capillary effect won't occur. Any spaces not sufficiently taped will pull in the paint, even against gravity. (Sorry to turn this into a physics discussion!)
Again, it goes back to properly applying tape or using a paint shield and then getting it away from the paint before it gets too tacky. And yes, weeks of leaving tape will definitely pull paint away.
And, to keep kicking this dead horse, when putting on the tape, be sure to limit how much of your fingers touch the sticky side... the oils from your skin will cause the tape to not stick properly. Most pros don't tape, but if you watch some that do, you'll see that when they tape manually, they won't apply the little 1-2" of starting tape because that's where fingers have torn it off. They'll use it as a tail and leave it dangling as a pull-tab.
Feel like you could start painting for a living with all this info??

Jim