Mysterious Stance says:

E commit, commit 1 foundation: When you could block during the Block Step of this attack, make a control check against a difficulty of X. If successful, this attack is considered completely blocked. X equals the speed of this attack.

Is X the attack's speed at the time you play the E, or at the time you are trying to make the check?

Yes x equals this attacks speed is reffering to this attacks current speed. Also x would be set when you play the enhance.

Possibly I am not understanding what you said, but the first and second sentences of your response seem somewhat contradictory to me. I will attempt to be more clear.

If the attack has a speed of 3 when I play the E on Mysterious Stance, and my opponent then raises the attack's speed to 5, do I need to make a check of 3 or 5 during the Block step?

If the speed is @ 3 when you play the enhance, you check against a 3. If the speed is at 7 when you play the E, you check against a 7. X is set when you play the enhance and x = the attack's current speed.

That is what I was looking for. Thank you.