The way I understand when you can hover is:
Option 1: Mewtwo hovers if he has his midair jump and hover, and on the first frame that he can input a jump after he finishes an animation (or the first interruptable frame of an interruptable animation) the jump button is being held down and is not released until the sound effect starts.
Option 2: Mewtwo hovers if he has his midair jump and hover, and is in a standard aerial state or interruptable animation and the control stick is down while the jump button is pressed and held until the sound effect starts.
(For either option you must be in the air the entire time)
The only way I know to lose your hover but not midair jump are using hover (for a very short time). Note that while grabbing a ledge refreshes your midair jump, it does not refresh your hover.
[collapse=Some things to support this view]
You can't hover immediately after walking off a platform or the stage with option 1. This can be explained by the fact that there is no animation for walking off a platform or the stage.
Since the first frame of the platform drop animation is the first frame when you can input a jump, you have to be holding jump on that frame to use option 1. If you jump, then hold jump to do your midair jump, then land on a platform and press down (while still holding jump), you will hover. This does not work if you land on the ground, because you are not in the air. On a platform, if you press down, you are in the air immediately.
You can use option 2 after dropping through a platform, because the platform drop animation is an interruptable animation.
You aren't in the air during the first frame on which you can input a jump after a grounded jump (an interruptable animation), which explains why option 1 doesn't make you hover as soon as you jump if you hold jump. Option 1 does, however, make you hover on the first frame after Mewtwo finishes his grounded jump (an animation) if you are holding jump.
(Theoretically there might be a specific frame after the platform drop animation where you could start holding the jump button without holding down and still hover. Of course, this would be frame perfect. I'm not sure it's actually possible, though, because you might need to already be holding the jump button on the frame in question, which implies that you would need to press the jump button after the first frame of the animation, but before the last frame, which would make you jump)[/collapse]
This is not a glitch involving hover. It involves the midair jump. After using (1) an aerial, (2) falling off a ledge without jumping, or (3) waiting a certain amount of time, before teleporting, you lose your midair jump. You cannot hover without your midair jump. As such, hover is only affected by this glitch indirectly.