I've loaded up some long videos onto my TinyTV2, and while they do "keep playing" while I'm on other channels as I'd expect, they always start from more-or-less the very beginning when I power the TV on. I understand that saving position would be tricky, and keeping a clock running while it's off would waste the battery, but personally I'd be happy with the solution of it just starting playback from a random point in the video every time it's booted, so I'm not always seeing the same opening seconds of it every time I turn it on? (I'm not sure what sources of entropy it would have to draw from to pick the random number, maybe the current battery level?)