We had to do carpets due to cat pee (the WORST!). If you really read the directions on enzyme cleaners, you have to follow them to a "T". The enzymes need time and the right environment to work. If they dry out, the enzymes die leaving the problem. So the area should be saturated and kept wet and oxygen-free by using wet towels, etc. for at least 24 hours; more if necessary.
Not sure if your recliner will be okay being kept wet. If it can't, I would say it's going to take several applications to accomplish the same thing.
Good luck - gotta love a sour recliner!