The power control line for your power supply requires a maintained contact to ground to remain powered.
There are a few options that you can use.
1) Use a toggle switch or latching push-button switch.
2) Use an alternate-action latching circuit to convert the momentary signal from your switch to a latching signal.
If your momentary switch is floating, there is a simple circuit that works well. What I mean by "floating" is that both sides of the switch are completely isolated.
The reason I mention this is because sometimes, you need one side of the switch to be connected somewhere else, such as ground.
simulate this circuit – Schematic created using CircuitLab
This is a classic 2-inverter alternate-action latch that I first saw in Don Lancaster's "CMOS Cookbook" back in the '70s. It works extremely well and can be very tiny - some of the new "Tiny Gate" logic contains both inverters in a single 6-pin package.
My only changes to Don's circuit as published is to add an extra RC filter to the first inverter. This has two benefits:
1) Reduces the possibility that impulse noise (static discharge, etc) can change the state of the latch when not desired.
2) Provides a defined output logic state when the circuit powers up. You can connect C2 to Ground if you want the latch to power up with the output LO or have it tied to the V+ rail as I have shown if you want the latch to come up with the output HI.
I assume that you want the power supply to remain OFF when connected to the AC mains, so I have shown the latch to power up that way.
The chip needs to be powered from the 5V standby power lead from the supply.