Which CPS did you use? I would suggest starting with some monitoring. I would want to watch IPR duty cycle, ICP pressure, and fuel pressure.
There are several possibilities. Your statement that it takes 30-50 minutes to re-start would point to a failing IPR coil. They get weaker when warm and when they are failing, they will lose their "grip" on the needle and the engine dies. After the coil cools down, it will grab again. RPM shouldn't matter, but maybe that's just a coincidental observation.
Another possibility is the HPOP isn't being fed as fast as oil is flowing through it. A bad supply (low pressure oil pump) or a high output situation (ruptured injector O-rings) could contribute to that scenario. With this theory - time shouldn't play a factor in when it will re-start.
One question - when you re-start it after the 50 minutes, does it start normally or do you have to crank a lot? If it starts right up, I'd bet on the IPR. If you have to crank a lot, I'd go looking at oil issues.