The last few weeks I've seen a number of clients that do a lot of core work, or by the nature of their daily activities, they use their core a lot. Many of them think they have a weak core, though the core muscles seem toned. There's few things that could be happening:
If you are doing core exercises (not under the care of a licensed healthcare professional) and are feeling more discomfort rather than less, it might be helpful to stop doing them and focus on flexibility and mobility for a while. Have a physical therapist evaluate whether you need the exercises and if they are being done correctly..
Here's one view of why you need to be able to move as well as stabilize your core. Qi gong, tai chi, and yoga can help you keep it that way.