The nerves from the low back (mainly L2 and L3) control the muscles of the hip flexors and quadriceps. It sounds plausable that you may have some compromise to that activity and as a result the quads strength is being inhibited during exercise. It may in fact be there all the time but it is only during exercise that you notice it. If you go to a good physiotherapist the first thing they will assess is your neural function in the lower limbs. This will assist provide some insight into this issue.