If there is a problem with your approach, then definitely get that worked out as GTGT has stated.
However, if you are truly having issues with the shoes, here is what I try to accomplish. I use the sole to determine my slide. I try to have a sole that does not make me stop, yet not slip also. I use my heel to stop. If I am sliding okay, but my heel is not stopping me, then I need a "stickier" heel (the opposite is true for stopping to quickly). This at least seems to be some of your problem. You are sliding fine (no off-balance issues before trying to stop) but your heel isn't stopping you in time.
One thing to be aware of. If you have been using the same sole and heel combo for a long time, they may actually need to have some maintenance done on them. Everyone is different, but if any part is rough leather (suede-like) then an occasional brushing would be good. If any part is rubber (Goodyear type), then the occasional lite alcohol treatment can keep the traction normal. If it is somewhere in between (most heels are a type of rubber) then you will want to periodically remove any residue that accumulates (I will rub it on the carpet by simulating a lite sliding motion). Be careful though since dirt and dust on soles will cause you to slide more and cleaning a large amount of this off your heel at one time will make you stop faster, maybe too fast. So you may need to work in the heel some outside of competition.
And lastly, work in all of your soles and heals during practice sessions. You don't have to actually bowl with them, but at least wear them and simulate using them. This way when you need them, and you will at the most inopportune time, they will be ready to use without any breaking in.