This is interesting - and shame on me - I'm pretty sure I have given "advice" in the past that re-annealing would not cause any damage and probably thereby insinuated that it would make no difference if you re-anneal a piece of brass multiple times - as long as the temperature and time does not exceed the "normal" annealing temp and time.This is from FAQ on the AMP site.
Our target annealed hardness for all brass is 100 Hv. Provided the necks are harder than this to start with, that is what our programs are calibrated to deliver. If the same case is then re-annealed after cooling down, the neck hardness will drop slightly by approx. 4 Hv. The brass will still be fine, and when shot and resized it will come back to regular hardness. For absolute consistency we wouldn't recommend including that case in your match ammo, but it will be fine next time around. If the same brass is re-annealed when still hot, it will probably be ruined.
It would be interesting to see what the effect on seating pressure is, and whether that 4Hv would become 8 and then 12 if you kept annealing - and if it is something you just see with induction annealers (which would hint at a conductivity change in the brass with each subsequent annealing?)