The problem is that your flushometer valve could probably be in need if servicing, in many cases this will fix the problem. Valve specific repair kits are available. The labeled parts #7, #13, & #16, in the generic diagram below should all be replaced to ensure proper operation. The Parts on the upper right side above the vacuum breaker label are the stop/check valve. This is not normally replaced as it is the point where the flushometer valve is isolated for servicing. A screwdriver is usually the tool required to shut the stop.check valve off.
There is also a possibility that these parts will not fix your specific problem. The flushometer if flushed while the water is off will cycle 1 time when water pressure is restored. If the water supply for your building is inadequate to support the volume of all these flushometers triggering at once some of the flushometers will continue to run. If this is the case a plan to resolve it would be the installation of more valves to isolate smaller areas of the building so that pressure drops do not occur. This would be a good idea anyhow as it is always a good idea to have as few people as possible affected by a plumbing emergency. Usually all that is required to restore the valve to proper operation while it is running as you describe is to turn it off at the stop/check valve and turn it back on.
The theory of operation of this valve is a little difficult to grasp but essentially water pressure is built up in the area under the #1 & #2 caps above the #7 diaphragm and relief valve in the center of the diaphragm by water that flows through an orifice in the diaphragm. This holds the #7 diaphragm and relief valve down against the sectioned valve body. The outer ring of that valve body is the incoming water supply and the inner ring is the water that is discharged into the bowl or urinal below the valve. The diaphragm against the partition between the inner and outer ring is what shuts the valve off. The downward pressure is greater than the incoming water supply because of the hydraulic principle where the larger dia. cylinder under the #1 & #2 cap is larger than the area of the ring where the incoming water supply is located.
When you press the handle there is a plunger that pushes on the lower stem of the mushroom shaped relief valve which is in the center of the #7 diaphragm and relief valve pictured above. This tipping allows the pressure built up under the #1 & #2 caps to run down the tube of the #7 Diaphragm and relief valve into the bowl or urinal below. This release of the pressure allows the #7 diaphragm to spring upward and opens the flow of water into the bowl or, urinal below. The water then flows through the orfice until the valve closes again when the pressure has built up under the # 1 & #2 cap.
In your case with a low water supply pressure there may not be enough pressure under the diaphragm to flow water through the orfice. The water going through the orfice is caused by a backpressure of the water flowing down into the bowl or urinal below. If the flow is not high enough to generate this backpressure water will not flow through the orifice.
If the orifice is blocked by scale or dirt water will also not go through the orifice.
Did you get that explanation? Probably not but maybe the super will!
In any case I'd try to get the existing flushometer operating before making major changes.