I would guess it might be be too few tetras in too small a tank. When I read care guides I always used to wonder why tetras have comparitively massive tanks for such tiny fish. My guess is sometimes they need to avoid the rest of the shoal because of breeding and pecking order politics. I also wonder if they naturally spread out into hiding places when they sleep, and the neon stripes (on neons and related at least) is what they use to shoal up for safety when they are in the open looking for food. My cardinals do not seem to require the "swimming space" people say they need for swimming unless they have just been fed, I think it's because while they need to know they are in a shoal for safety, they also like personal space from time to time.
My guess is the other two have bullied it, and the stress is meaning it's eating less and is more sensitive to water pollution. Seriously Fish suggests a three foot tank for rummies. That seems a little extreme to me, but I have to admit Seriously Fish is more likely than me to be right about things like that. I have never kept rummies. If you only have three I suspect you only have a 5 gallon tank or so and were sensible enough to limit the stocking. I have read a minimum of 6 is needed in a shoal, and that they can't count more than 6, but in my limited experience tetras seem to get happier and healthier the more there are of them.