Hi ... it sounds to me that this sagging is cause by wear and tear - at some point the rotation of the door handle is converted into a linear movement. Many common handles have a square shaft which fits into a plate which rotates via a square "hole". It would seem as if this square "hole" is being converted into a "round" hole by share force over the years. Suggest replacement parts are needed.
I suspect that my technology for upvc door handles is not upoto date ... but these comments might be of help.
Nyge
March 2011