ATX PSU turns off under heavy 12V load, unless increased gradually
Load transients are limited to allow for more efficient power supplies.
The electrical specifications for your PSU should list what they are, and system builders need to verify that the PSU capabilities meet the requirements of the mainboard, just as they do for maximum current.
For example, Intel's power supply design guide lists transient slew rates of 1.0 A/μs, and a step size of 40% on the +12V1DC rail as required from a compatible PSU.
If your PSU can deliver power to a mainboard as specified, but go into protection mode when connected to your load, then it is likely that you have more stringent requirements on the PSU than a mainboard would have, so either you need a PSU that meets these requirements, or you redesign your application to relax them, e.g. with capacitors up to 3,300μF that are charged during the inrush current limited phase while the PSU turns on.