The thickness planers I've seen have a cutter head between two rollers. The rollers grab the stock and feed it past the cutter head, counteracting the force applied by the blades. If the rollers do not have a secure grip on the stock, the cutter may kick the piece backwards if a blade catches.
(Source: https://en.wikipedia.org/wiki/File:Thicknesser.gif)
What safety risks does this present when planing short stock? How can I determine the minimum length which can be safely planed?
It varies by model, check the manual online for the model you're looking at. Generally the shortest recommended length is also the distance between the center of the rollers.
Basically, you never want the possibility of a piece of wood being 'stuck' under the cutter head but not being held down by a roller.
You can counteract this limitation with some variation of a sled that holds short stock securely to the bottom with sacrificial 'rails' that ride the rollers and get planed down with the short stock itself.
Technically there's no minimum length you can send through a thickness planer if you 'cheat'. There are various tricks that allow planing of material both too thin and too short and they can work well.
For short stock you use outriggers, pieces of scrap wood glued to either side of the board you want to plane. Like this:
(Source: http://www.diynetwork.com/how-to/how-to-plane-short-boards/index.html (archive))
After you've planed to thickness you simply pop the outriggers off with a chisel.
As a rule of thumb, i never plane anything shorter than 12". I have the Dewalt DW734.
From experience of a few different thicknessers, I'd say no shorter than around 300mm (approx 12").
It's worth noting though that if a piece does get stuck (i.e. the outfeed roller doesn't have a good enough grip to pull the piece all the way through) then you can often push it through with the next piece you are thicknessing or with a thinner piece of timber.
I don't think I've ever had a piece "kick back" out of the thicknesser as the infeed roller seems to stop this. I have however had pieces of timber "explode" but this has always been because there was a split in the timber or I was trying to thickness it to too small of a size. The pieces ejected were not travelling at what I would call dangerous speeds, however as with any woodworking machinery I would advise the use of safety specs or goggles.
