I'm having trouble putting my finger on clear guidelines for choosing when to announce a power down, and would love to hear some analyses.
There are several things to take into account:
Your position in the race. If I 'm comfortably ahead, I will be somewhat more inclined to power down (willing to accept a known handicap rather than possibly risk an unknown turn of events if I take much damage quickly). If I 'm trying to catch up, I will only power down if it seems my progress is getting way too slow due to locked registers.
Terrain. Contrary to other answers, I will be more inclined to power down on conveyor belts that take me closer to where I want to be. I might even power down when I normally would not consider doing so, because it's unlikely that I would be able to effectively utilize all 5 registers while at the same time staying on the belt. From that perspective, it costs less to power down in this situation. Of course all of this assumes that I will stay on the belt, which brings us to...
Proximity to other robots. Obviously powering down when near other robots is risky, even more so if there is deadly terrain nearby. In this situation I would consider powering down only if in imminent danger of being destroyed, and even then I might risk it if my last archive was close by.
I don't think about powering down until the first register is locked. If the number of robots in the field is low, I might continue one or two turns, but if the number of robots is more than four, I will power down.
When I announce my power down, I will try to move away from the clutter of robots to avoid a possible death. And I will definitely not power down on a conveyor belt, but that's just due previous experiences.
A key question is whether you'll do as much missing the first of the next, say, three turns after powering down as you would have done with all three turns.
I have found that it's clearly wrong to announce when I am expecting to have only 2 damage, and probably wrong when I'm expecting to have 3 damage. I don't have any probability analysis to back this up, though.
If I'm landing on a conveyor belt that will take me closer to where I'm going, I am only slightly more likely to power down. I recommend against overemphasizing this (conveyor belts concentrate robots, and people might push me off or shoot me while on the same conveyor belt).
If I'm expecting to be in the "thick of things" at the end of my turn, I may end up with nearly as much damage as I started with, so I would almost not power down at all unless I am expecting locked registers. The loss of control for a whole turn can be very damaging.
If I'm going to be in an area difficult to leave (such as being in between conveyor belts that point at me, and needing move 2 or move 3 to make progress) I am more likely to choose a power down.