As far as I'm aware, registration is required every night, though as Fluffy says, if you keep your train ticket, that will be fine for the night you're on the train. At any rate, to avoid problems, you are best off staying at a registered hotel or guesthouse every night (provided you stay somewhere registered, and every place mentioned in the LP is registered so these places are not particularly hard to find, the hotel or guesthouse will arrange all the registration for you and give you little slips of paper which you need to keep; registration in Uzbekistan isn't as daunting as it sounds).
Giora