Steve,
A couple of areas to look at. First, take a look at the CAT menu, and see what your update frequency interval is. I use 20 Hz for SSB. That gives a smooth tracking, and once netted, SATPC32 will track through a full pass. It WILL update every few seconds, but the jump should be small enough that it is just barely audible. You can get by with a much larger step size, but of course the jump will be more noticeable, but still usable.
Are you using a USB serial port, or a "real" port? There is nothing wrong with a USB serial port per se, but some of them are rather flakey. I had one which required about 5 times the recommended CAT delay to work at all, and would usually eventually cause the radio to lose tracking exactly as you describe. The was not a problem with SATPC32!! Nothing else worked reliably with that port either, so I finally gave up on it and went back to a real serial port, since I had one to spare.
Alan WA4SCA