When an office chair starts sinking down the cause is the cylinder valve leaking and if it's an expensive chair you can usually buy a new cylinder to replace it.
But if it's a cheaper office chair it's not worth replacing the cylinder in the chair.
Instead here's what I did to fix my sinking office chair.
I took a hose clamp that has a screw on it and then put the hose clamp over the top part of the cylinder and then slid it down to the wider part of the cylinder itself and then tightened the hose clamp down.
That keeps the chair from sinking down and I was able to save the chair because other than the cylinder sinking down the chair was still in good shape.
I don't really use the cylinder to move the chair up and down anyway so it's not an issue.
But if you do need to change the height of the chair just loosen the hose clamp and move the chair up and down to where you need it.