I was wondering, how is it that boxers reactions times become slower as they age, yet if you see old martial arts masters, they still seem to have brilliant reaction times? Could it be because you take punches to the head?

maybe, combined with the fact that all that martial arts garbage is choreographed. Everything is passive in martial arts so it's faster by default.

Too many martial arts films and this is what happens.

I'm not sure this is always true. Perhaps some really experienced boxers also know how to mess with you technically enough to respond calmly without any need to rush anything. They are more relaxed. However those of us who are less experienced can not see as many opportunities and do not have as many tricks up our sleeve so we need to be quick to make advantage of the little we know in comparison. We spar competitively because we are always being challenged while the old masters can just play with their students and laugh!

perhaps it's more that they see the change in the entire body more and not as much their reaction time?