Also it's not a physical strength thing I don't think. I also run on a regular basis and my thighs and core muscles are pretty strong from that.
I agree with the notion that it is muscle fatigue. This could be remedied by making adjustments to the binding positioning/angle as suggested.
People often make the same assumption the original author makes here. In no way am I challenging the claim that you are physically fit, but keep in mind that being fit for one activity is rarely related to fitness for another activity. Try swimming a mile and tell me how winded you are (if you don't normally swim).
My point is that even a strong quadricep muscle that can bang out a 5k will start to shudder when locked into a -15 rear binding position trying to keep an edge on a gritty, icy black diamond. Sometimes, especially when still adjusting to the speed of riding, the individual doesn't realize how tensed they really are.
My buddy came riding with me for his first time a month ago. He did pretty well, we even took him down a couple blues. As I would gently transition from edge to edge falling down the hill, he was flexing and working much harder to maneuver and control the board. Part of this is the experience I have that he lacks, and another part is the conditioning of the muscles for that specific sort of movement and load.
If you still experience a similar feeling of fatigue or exhaustion after adjusting into a more comfortable stance, I wouldn't worry much more about it. Really work that leg, and take a break when you can barely stand. Situations like these are also good times to practice riding switch.
I remember a spent a whole day practicing butters and presses. My leg felt like it was experiencing a siezure by the end of the session.