I bought a couple of A560s a couple of months ago and tested them - the batteries seemed to drain almost right away which is why I discounted them for this. My intention would be to use the lithium batteries for the actual launch, the expense has put me off trying them beforehand though.
As noted by others, this shouldn't be the case if everything is working properly, but they are prone to bad contacts. The life of these 2x AA cams with good NiMH cells should actually be better than some of the small lithium batteries like NB-11L. This is reflected in the Canon CIPA specs. Even though your usage will be different from what the CIPA test uses, it should give you rough guide to the relative capabilities.
Note that the life with alkaline AAs is
much worse in the AA cams.
In the timelapse testing I've been doing recently, my D10 (NB-6L battery) seems to top out around 6500 shots / 140 minutes.
With A540, I've never actually drained a full battery doing timelapse, because it doesn't support SDHC and the non-HC cards I have are only 2GB. I have got ~5000 shots with significant battery remaining.
Both of the above are shooting nearly as fast as the camera will shoot, with the display off.
The smallest cameras seem to be the ones that have the battery 'built in' - I can test these in a freezer but I'm wary that the batteries won't operate at the -50C it can get to at the top of an ascent (which is basically where you want the camera to work the most).
All the battery technologies will have greatly reduced capacity a much higher temperatures. Even at 0C, battery life will be much worse. Fortunately, the camera itself puts out a fair bit of heat, so if it's well insulated, you may be able to keep it from getting so cold.
That's a pity (would have saved some time 
) I'll look through some of the literature - in the meantime are there any that you would say 'definitely avoid' or any that anyone here has had personal trouble with?
Not really, there have been other problem ports, but there's well over 100 ports and I don't know what state they are in off the top of my head. IXUS300/SD4000 might be one to avoid
http://chdk.setepontos.com/index.php?topic=12198.0I did the IXUS140/ELPH130 port, it seems to be pretty functional and is fairly light weight, but has pretty poor battery life.
If you post a short list cameras you are considering, we might be able to offer more useful advice.
