Since you say the springs all seem to be in place, then maybe they are weaker than they should be. Another possibility could be that the drag adjustment, if the chair has one, has loosened. Look for wing nuts near the rear of the mechanism, one on each side, that would adjust pressure on some coil springs. Turn the wing nuts to compress the springs on each side, just a full turn or two at a time, as this will also increase the force needed to recline the seat back.
Furniture Medic by Randy Buchter, January 2012