I'm pretty sure it's a lot faster than 10-15 minutes.
I've had chests despawn while I sorted through inv looking for trash pots and food and junk to sell to my vendor or delete.
No one knows how this works, and I don't think that ZOS has ever confirmed (or denied) any of the theories presented in here.
That said, it looks like there are only so many untouched chests that are spawned into a zone at a time. This is some number that is less than the total number of places where a chest can be located. Theory is that the game checks periodically to make sure that there are chests to be looted, and if the number of chests drops below a certain level, new ones are spawned into empty spots to bring the total untouched chests to the right number. I think that part of this includes some measures to despawn partially harvested chests, if they start to pile up. Again, ZOS has not said boo in support, or disagreement, with any of our crazy chest theories in here.
All of the node timing tests were done on PTS, as far as I know. This is the only place where partially harvested nodes will hang around long enough to despawn without a player running by. This is long, boring research, by the way. I did some of that research.