Serving should last much more than 30 -40 shots before it starts to wear and seperate. I can think of a few possibilities to cause the problems you're having. One possibility is just a bad serving job on the string. Another is a burr or rough spot on the "claw(s)" that hold the string. Another is twisting the string the wrong direction to adjust length (shorten it).
The bad serving job is unlikely, but it can happen.
The claws can be cleaned up with some fine sandpaper if they are rough.
The string serving is wrapped in either a clockwise or counterclockwise direction. Hard to explain, but if you look closely at the direction it is wrapped you will see the string needs to be twisted in the same direction when adjusting length. If you turn it the opposite direction it will be causing the serving to loosen and will cause problems.
All I have on hand is a longbow string, but here's a pic to illustrate what I mean:
If it's a flemish twist string you must twist in the same direction the loops are laid (wrapped) - if the serving is twisted the wrong direction it will loosen. That is the stringmaker's mistake! If that happens all you can do is re-serve the string wrapping the serving in the proper direction.