Interesting find! I can't say for sure why it happens from just the video. Can you email the project? Please let us know how to find the key you are moving.
No curve line appears between keys in the dopesheet when the value is constant during the time between the keys. In your case, the key before the key you are moving is Bezier. For the value to be constant, the Bezier handles need to be exactly horizontal. Moving the keys apart should not affect this, so it will be interesting to see why it does.