There is research out there on IQ stability, but I'm going to focus on some qualitative observations for now.
At this point I've worked in secondary schools for long enough to see two, three, four, or more cognitive assessments of the same child for many, many students (and even to have assessed some of them multiple times). I have absolutely seen many LD kids show drops in IQ over time, in language, perceptual, or both. I have also seen quite a few children with early language delays who looked intellectually disabled in the primary years, but turned out to be at least average in intelligence, once they had overcome those early s/l deficits.
I think there are a couple of primary factors involved here: first, of course, there is regression to the mean, which would predict that extreme scores (high or low) would become less extreme on subsequent re-testing. Second, there is the impact of early environment, which is huge for preschool and primary achievement--and, after all, cognitive assessment is unavoidably a form of achievement testing that attempts to sample skills that don't usually receive direct instruction, as a proxy for native learning ability. Then, there is the plasticity of the brain, and the possible changes in brain development that might occur as a result of the early environment--whether due to nutrition, stimulation, access, trauma, etc. Associated with plasticity is innate developmental courses, which differ from one person to another.
Under optimal circumstances, IQ is fairly stable from age 3 to adulthood, but what is "fairly stable?" Antisocial/prosocial personality traits are equally stable from age 3 to adolescence/early adulthood (e.g., predictive of juvenile delinquency), but instead of immediately locking away mean preschoolers, we try to teach them--and do succeed (not as often as we should, but that's another story for another day) in modifying the trajectory of some of them in a healthier direction.
The existing instruments are relatively high in reliability, with test-retest numbers usually in the .90+ range for global scores, but as others have mentioned, they are not designed to account for life. The bottom line is that cognitive assessments are samples of behavior that we associate with an abstract quality we call intelligence, but there is no way to directly measure intelligence entirely free of environmental factors. This is why we can only use tests with individuals who have membership in the normative group of which the standardization group was supposed to be a representative sample. Except that anyone who is EG/PG or 2e is by definition not well-represented (or represented at all, really).
