My Keling KL-600-48
Switching Power Supply, Keling Technology Inc, USA power supplie's fan is on full time and the PS never heats up.
A solution for you is to look up the specs of your power supply, if you have a multi meter test the Volts from the connecter, check the required supply for the fan and if both are the same and the connector fits the fans connector, and your specs suggest fan needs to be on then it looks likely that the connector fell off or as you suggest the tension on the cable tie most likely just disconnected it.