Perhaps, but probably not without a little help. Studies show that a loss of muscle strength and power are typical after unilateral knee replacement (UKR). UKR refers to the placement of an implant on one side of the knee (either medial on the inside half of the joint closest to the other knee or lateral on the outside of the joint). Walking speed, recovery from falls, and stairs can all be affected by persistent muscle weakness after this procedure.
The loss of muscle power affects muscles on both sides of the leg (front and back/extensors and flexors). It’s possible for the nonoperated (stronger) leg to compensate for the operated (weaker) leg when walking but it takes more muscle power than that for stairs. Stairs require the use of both sets of muscles and in both legs at the same time (the supporting leg and the moving leg).
It’s good that you haven’t just accepted this as the way it must be — you can improve your strength and get a normal stair-step pattern back. And it’s a good idea to address the problem now before it becomes even more long-term. All evidence to date suggests that your loss of strength won’t go away on its own — even after waiting months to years. You may need to consult with a physical therapist who can identify which muscles are affected and prescribe the right exercises to help with full recovery. Until you get your complete motor recovery, you will be at an increased risk of falls and injuries from falls.