Although a bit dated, the link below has some interesting info on the general stability/growth of the GRE score over time. It shows some change over a ten year period, but only approximately half a standard deviation on average. Given the extreme scores often looked for (I'm familiar with old GRE scores), that's only 25% of the difference between mean and /minimal/ cut points for the GRE (p.20). Conversely, Wilson notes that gains obtained are typically small for short-term retesters (a population described as those wishing to increase their scores) as a function of regression to the mean (p. 21). Again, dated data and I didn't spend a ton of time reading through it, but GRE scores tend to be fairly stable, likely as a function of general aptitude.
https://www.ets.org/Media/Research/pdf/RR-88-39-Wilson.pdf
I was trying to find some more recent data from independent researchers (seems a reasonable thing on both accounts), but my 30 second google-fu didn't perform as anticipated.