So, an update here...
Before Christmas I picked up 10 red cherry shrimp from the LFS, acclimatised them and then let them loose in the tank.
I suspected that over Christmas I lost a few, as I barely saw more than four out in the open at once, though no bodies ever turned up. When I was cleaning, I tried not to disturb the tank too much, but a fortnight ago I decided to go looking for them as I thought all of the shrimp had died. I found two, but one died last week and the other was found dead today.
I've had plenty of algae (sigh) for them to feed on, and I've been adding some dried shrimp food pellets I got from the LFS. The two that died most recently had reached a good size and were a bright red colour, so I thought they were just hardier than the others. I had plans to add more shrimp at the weekend, but having had the last one die today, it leaves me suspecting that any more shrimp I add to the tank will meet with the same fate.
I've checked my tank's water and it is the same as it usually is - 0 ammona, 0 nitrite, 20-40 nitrates. I'm in a soft water area, but having looked into the red cherry shrimp, I was under the impression that the soft water shouldn't have been a problem.
Have I gone horribly wrong somewhere, or is there another reason to consider that would explain why ten shrimp have died in just over a month? The shrimp I have found bodies for don't appear to have been attacked, and while I'm no expert, I haven't seen any sign of disease in them.