Like I said, in this context, "energizer" sounds like some sort of power transfomer in the system, converting the raw power from the main power plants to something more usable to, say, that computer terminal on the table, or the transporter. Kinda makes sense the suckers'd blow under those circumstances.
Also makes sense, then, that dilithium crystals would be involved. Ever since "Mudd's Women", we have known that the ship's power flows through them (but apparently doesn't emanate from them). The dialogue of ST2:TWoK also suggests that the energizer is a tight bottleneck of some sort that can be quickly repaired by a brave hand, rather than a major component - and "manually realigning dilithium crystals" is a perfectly valid explanation to what Spock is doing in those scenes, as he operates on a device not too unlike the dilithium cradle of TOS.
OTOH, "energizer" could also be a device that nurtures the dilithium so that it can do its job. Nonenergized dilithium is no good, as we learn in "The Alternative Factor". The non-main energizer that is used for restoring the dilithium to working order in that episode could be an "intensive care unit", while the main energizer is the device that does the constant nurturing when the crystals are at work in the actual reactor.
So perhaps the closest analogy would be a preheater in a sodium nuclear reactor? If the sodium is cold, nothing works, as the circulating fluid isn't fluid any more. An auxiliary preheater would be needed to get the sodium circulating initially, after which the main heat exchanger would make sure the stuff didn't freeze solid during regular operations.
Or it could be llike the hydraulic compressors of an aircraft. A separate APU is needed for "priming" the hydraulic fluid, giving it initial pressure, so that the main engines can be started. A component in the main engines then takes over the task of pressurizing the hydraulics, of "nurturing" them.