when people are tested repeatedly they learn the demand characteristics and become better at performing IQ tests.
many of these tests are available in some form online as a game or puzzle, or a total reveal of something that was quite guarded from general knowledge. the cat is out of the bag, IQ testing needs to be redeveloped.
If this is correct, there should be statistically significant evidence that IQ scores increase with the number of IQ tests taken. I personally have never seen any such study results.
it sounds like there is an experiment to be designed on this basis. One thing that comes to mind, is my experience with IQ estimation tests, is the question or concern the tester had regarding any past testing, there was a very different heuristic for people who have had even one previous test.
I have been tested on 6 occasions each estimate at a high percentile, we would need to find someone in apx. 10th percentile and follow thier score distribution as a function of test frequency, with some non trivial considerations for experimental controll of confounds.