The older HF saws were really good ones but unfortunately the "newer" ones (some as old as 5 years) have really crappy gears that tend to wear out in a hurry. Wash that gunk out with Kerosene, mineral spirits or diesel fuel and then closely examine the gears and the bushings where the worm gear ends go through the box. If the teeth are excessively worn or broken and/or the bushings are worn out that can cause the symptoms you mention. This has been a serious flaw in the newer version of that saw, from about 5 years ago up to and including the ones they have now, and if the gears are excessively worn and/or have broken teeth it very well may not be practical to repair. The worm gear and shaft bushings however are an easy repair if that is the biggest problem, if they are worn the worm gear will slide slightly and the gears will not mesh properly causing that skip you described..
Kind of a coincidence this has come up because I have been meaning to mention this very problem since I have recommended the HF saw several times here in the past, but no more! FWIW, the Clarke brand saw at Northern Tool appears to be identical to the old saws from HF and they are priced about the same, they may be the same saw but I can only say they look to be the same. In any case I have to do a 180 on the HF saw and take back everything good I said about them, the saw they sell now is not the same saw they had 10 years ago when I bought mine.