Power supplies are rated by their maximum DC output, so at true full load you will be pulling a few hundred watts more than the label rating due to efficiency losses.
You're likely exceeding the current limit for one of the 12v rails which causes the shutdown.
Hardly any modern decent high wattage PSU has seperate regulated 12v rails =)
In fact, I think no decent high watt PSU has seperate rails. That was a huge fad that kinda disappeared.
Also, to the OP... you arent tripping your mains breaker are you? thats pretty close to a 15amp limit on 110/120v mains...
Another thought is, some PSU's hate being heavily crossloaded(no / little power being used on either 3.3/5v & almost all being used on 12v or visa versa) .. usually this just results in overall effeciency drop, but not complete shut down. This is rarely seen in highend 1kw+ PSU's