I see lots of woodwind instruments in my shop that arrive with cases that are in need of help as much as the instrument they are trying to protect. There are faulty latches, improper blocking, and a myriad of loose reed cases, mouthpiece caps, swabs, gum wrappers and lots of other junk that has no need to even be in a case. The truth is that much of the damage done to your flute, clarinet, saxophone oboe or bassoon, happens inside the case while the horn is being transported back and forth from rehearsals and performances.
Make sure that you don't overstuff your case with books and music. It stresses the hinges and can damage the key work. Get rid of the old reeds and reed cases. Keep the saxophone mouthpiece and neck secure and wrapped.
Finally, see if your instrument moves from side to side in the case. If it does, try shimming it with a cloth, some folded blocks of cardboard, or some other non damaging material to keep it still.
A bit of attention given to your case will help keep your instrument functioning well.