The first 're-case coloring' is also (at least) it's second.
We used to do many actions and parts a second 'redo' time as customers weren't happy or they just didn't come out well enough anyway to suit us.
Lots of previously re-done actions were re-done again. Most of those at the time had been redone with a cyanide process and the customers wanted the bone-char look instead. So this was at least their 3rd time in the fire and quench.
Complete annealing and polishing was always a key to good results.
However, the look of the resulting colors wasn't always as predicable, maybe as bright or the colors as correct would put it better, as the # of times the part was re-case colored increased.
That may have been just that particular process or something with in it. There are so many variables to get to the same end result that one may fail when others succeed.
As far as resulting in a piece that was more brittle or warping of the parts occurring in the multiple redone parts as opposed to those just redone once from original (as far as you'd know!) , I can't ever think of any out of the ordinary problems in that area.
There is always the chance of warping, that just goes along with the process no matter how it's done if you want hardness and colors together.
Straightening any slight misallignment is part of the job and not that hard. It doesn't happen all that often and the folks doing the work these days have it pretty much under control.
It's the wild pretzel like twists and over hardened thin parts that'll quickly put the project into the small parts bins.
Just my experience.