A Master cylinder shouldn't slowly sink, no matter what !
A trick that mechanics do when changing disc pads and shoes etc is to push the pedal only half way, and then repeat this. If you push the pedal all the way you may push the rubber seal over any debris that can accumulate in the bore of the master cylinder.
Most mechanics have had to replace a master and learn it is easier not to push all the way to floor unless the master cylinder is new ....
I suggest replacing the master cylinder with a quality item and get the brake system power bled.
Ian
Bittern
