SAT is very g-loaded, so it would be susceptible to the same practice effect that IQ tests in general are susceptible to. If you look at SAT/IQ tables, the 20-40 point increase Tyler cites corresponds to about 1.5-3 IQ points. This is consistent with the typical magnitude (< 5 points) of the practice effects on IQ test scores. Your "hundreds of points" are wildly inconsistent with this. The only way I could see that happen is if quite a bit of the SAT would test for skills that can be practiced but don't correlate with g. Not very likely.

The way to reconcile your experience with the evidence is to note that the score on a low-stakes practice test is just not comparable to the score on the real thing (with or without test prep). It's not that implausible to believe that, say, 10% of people (more than enough to account for your anecdotes) will score at least 100 points less on an early practice test than they could score on the real thing at the same level of preparation. It's hard to trick your brain into believing that something is high-stakes when it isn't.

ETA: On reflection, the low-stakes hypothesis probably doesn't account for too much of the puzzle. In particular, it doesn't explain any gain between consecutive low-stakes practice tests. I think James Miller's explanation takes the cake. The SAT-g correlation is likely a lot lower for a population not proficient in English.