In addition to the above, there is an adjustment for wear in the pushbutton latch that might help. If you look at the edge of the door, near the latch, you should find a little rubber hole cover. Underneath that cover is a linkage with an allen screw. If you adjust that linkage, it can sometimes help. This is the linkage between the handle assembly and the latch itself. It will help if the outside handle does not work well, but the inside does.
However, be warned that if your door is getting very old and rusty, and has misbehaved for long, the handle assembly itself may be bending. The button you push actuates a lever which is hinged on one side, and tilts out to operate the mechanism. Eventually that can bend and break. Try to get as much oil in there as you can. Usually if you keep it lubed and adjust that linkage, you'll be good for a long time.
If you've waited too long and run out of linkage adjustment, You can repair this by taking the handle out and unbending the lever if it's not yet broken, but if the Jeep is old and rusty there's a very good chance you'll shear off the studs that hold it on. If you do have to do this, grind the studs level and very carefully drill into the handle, and you can retap it for a 1/4" coarse bolt. Be very very careful and drill slowly with a sharp bit, because if the insert you're drilling into gets too hot it will melt into the handle and spin, and you're finished if that happens.