Is the problem that in particle collisions you can't tell the input energies with the necessary precision, as was possible when the input energy was simply the mass of a known particle? I had been assuming that some kind of precise accounting was possible: mass A at velocity n, mass B at velocity m. Splat! Then various products smacking with measured energies into detectors.
The long answer I will have to compose.
In the case of a nuclear decay, you start with a precisely known amount of energy. Three particles come out: a positron, a nucleus (with an atomic number one less than you started with), and a neutrino. You can't measure the neutrino, and you generally can't measure the final momentum of the nucleus, but you can measure the positron energy very precisely, and from an ensemble of decays, you can measure that there's an unseen particle recoiling against the positron. (If you look at the angular momentum, you can see right away that a spin-1/2 particle escapes.) One of the things that makes this analysis much easier is that there's one particle missing, and that one is massless. The missing energy thus equals the missing momentum, which is a valuable constraint.
In the case of an electron and positron colliding to form a neutrino pair, the input energy is very well known. Unfortunately, you don't see anything coming out, because the neutrinos can't be measured, and there's nothing else to see. You have to get lucky and observe a radiated photon or two. If you know the final state is a neutrino pair, that's all well and good, but if you don't, you're up a bit of a creek, because the problem is underconstrained. Two massless particles can give the same result as a single massive particle...or seventeen particles of different masses, for that matter.
The problem gets worse if you're trying to sift these unknown particles out of hadronic events, where there are many particles in your detector. For one thing, the particles are not perfectly measured. The more particles there are, the more the uncertainties add up. For another thing, you can't always tell what the "flavors" of the particles are. Pions and K-mesons are notoriously difficult to distinguish, but the K is three times heavier than the pi.
That's not to say that these difficulties can't be sorted out. What it means is that some hairy statistical analysis is required to pin down such a beast. You would never be able to look at an event and say, "Aha! Two 100 MeV particles are missing from this event!" But with enough events, you probably could say something like, "Look at this shoulder in the missing PT plot! That's not supposed to be there. Damn it! Now I have to spend my weekend chasing down the bug in the analysis code. Are you sure there's nothing wrong with the pedestal subtraction circuits? Howard was screwing around with them, last shutdown..." Then, a year later, when you've decided that there is no bug in the code after all, you say, "Maybe something's there."