The generator may have done what it was designed to do but may not have ever been designed to handle the very large electrical load HVAC demands. I worked in a Tennessee 5 story 200 patient facility. We had a 200 amp generator. It would power lights and the emergency power receptacles, operate one of three elevators, power the kitchen and power the Boiler System, the phone system, Fire Alarm, and that was about it.
Poor design years ago can cause failures many years later. I'll give an example. Our facility had a generator and was supposed to be able to operate generator and boilers for almost two weeks from an underground fuel tank.
At some point in construction a cost cutting decision was made to use city utility water for the generator engines cooling system rather than a self contained radiator. Well one night the utility lost a \n entire substation which powered our building and as well powered the utilities pumping station for utility water. After about 30 minutes the engine tripped off on high temperature and there was no power for over 4 hours. You would think that would trigger a correction. Nope.
Here is a worse one. Same facility. The State Inspector Generals Office demanded a Sprinkler System {water not CO2} be placed in the Electrical Switchboard and Emergency Generator Room. We {the employees and our Boss} protested to no avail. This room had a 460 volt 2000 amp electrical system. The 2000 amp system needed because the HVAC Chiller pulled 1200-1400 amps on start up and about 300-350 amps for running once up to speed.
These type of systems will go down. If for example the unit tore up requiring a couple days repair there is a work around which is bringing in a flatbed tractor trailer with a portable chiller on it and hooking it up using the buildings electrical system and chill water loop. It takes 4-8 hours to connect such a system especially if it has not been done at the facility previously. You also have to allow for transport time as these type of units are limited and only in larger cities. Ours came out of Atlanta 4.5 hours away when we needed it. I think Miami also had one but under these conditions would be useless as it was an issue with power coming to the building. Under hurricane conditions I would expect a local utility would loose partial or all power. BTW local utilities are well aware of these facilities and their power demands and special requirements.
mr. mm has done his share of engineering and the stupid things people do is sometimes beyond belief.