To be fair you could always pull a "Tornado" and stick a "roll cage" style section around your robot that you can attach and remove between fights. Spinners do have a history of "Spazzing out" when they come in contact with another machine with dancing/flying around the arena etc, but if you can put a frame around your machine, you essentially nullify the the first couple of hits and give you a window to fight back. Against vertical spinners you are safe-ish, depending on how tough the frame is. horizontal spinners... I don't know, would have to see an actual fight where this was employed I think.

(Ps: Not trying to shame tornado, simply using it as an example because it is one of the most well known examples of active adaptation to counter weaponry between bouts)