hmm All AKG springs are designed to be mounted in the controlroom , it is a feature all their manuals brag about !
much better then those pesky plates they didnt make !
so there is something wrong with the internal mounting system in yours , it must have collapsed
i have/had a bunch of akg springs none of them did this neither did the masteroom spring i had for years
i never really used them all that much but i would recall if they were that sensitive .. actually the masteroom wasnt so great
I currently have Two restored Akg bx20e they are certainly ok and in no way sensitive to noise and unless you kick them you would never even know they are spring , time will tell if i love them and they love me or if i sell them
that said i havent hit them with ambient mega bass from the dual 18" dual 15" woofers that i have to set up in one of my rooms one day if i ever finish them

anyway you need to open yours up , its probably obvious whats going on , if your lucky its not the spring mounting itself
its the cage or mounts they sit in .
in an akg it could be isolated by rubber ,foam, strings or springs depending on what year it was made
the smaller ones like yours are worse - because they were cheaper and there could be anything holding the springs assembly up
but most likely grommets or rubber pads of somekind have given way over the years
let us know what you find
myles recently bought one like yours ( bx 10 ? ) that was sitting at my place for a time
myles wanna chime in about the mounting system in that one ..?