Or bent forks, or a badly torn up gear, or lots of other things.
Certainly change the fluid and make sure it's full, but that usually won't fix popping out of gear.
Does the car have a 4 speed in it, or a 5 speed? For a 2003, I'd assume it was a 5 speed.
The simple answer is just skip shift over 4 and not use it. I'd also toss a magnetic drain plug in and pay attention to any buildup, because a lot of metal buildup means things are rubbing and the transmission is not long for the world.
If you have to replace the transmission, get a junkyard transmission out of a wrecked car (enough body damage that it's clear why it's in the junkyard, preferably to the back of it). It's unlikely that a wrecked car will have a trashed transmission as well, but a car with no major body damage is in a junkyard either for the engine or transmission. The manuals usually don't die, but... still. Wrecked car. That shouldn't be particularly expensive, and just use whichever clutch is in better shape.