This looks like a switch mode power supply. If it's shutting down on its own or not starting reliably, that's often a sign that either the output has a problem, the feedback isn't working properly, or the supply's switch mode controller can't power itself reliably.
Check for short circuits on the output, like the bad output caps that duak experienced.
Check the electrolytic cap (startup cap) that powers the switch mode controller. The cap and controller are often nearby the power switching transistor(s). The big heatsink in the bottom-middle of the supply and the cluster of four capacitors with transformer looks like the general area of interest or the boards that wires from there go to.
If the controller doesn't receive proper feedback from the output, via opto-isolator or isolation transformer, it will shut down. Dead opto-isolators are a common failure point.
It's also possible that the switching transistor (or its support components) has a problem resulting in lack of control of the output.
Oh, since this power supply supports remote control, make sure that a configuration switch, jumper, wire, etc. didn't get altered, loose, fall off, etc., such that it's getting a signal to turn off.