I noticed yesterday that a few times when I did 3-turns at a moderate speed, the blade would jump off the ice at the hilt of the 3-turn, and then I'd land and complete the other half of the turn.

While I was quite impressed that actually worked, I would like to know what it was I was doing wrong to cause that... Is it a matter of angle or body position, or am I moving somehow that I'm not realizing?

3-turns get jumped when one rises from a bent knee and initiates the turn too quickly.

Or possibly if you're forcing the turn with your upper body/arms. Generally if you're rushing the turn.