Premiere needs a basically perfect signal and perfect Internet access, so I would check those things first.
For me, any kind of intermittent drop-outs in Internet can potentially cause my Premiere Elite to reboot. Luckily, this almost never happens after I upgraded my router and cable modem.
You might want to get a Cox tech out to troubleshoot signal issues. Premiere is pretty touchy when the signal isn't just right. Too strong? Reboot. Too weak? Reboot. It is almost laughable.
Also, the "all channels go black" is a thing with Cox tuning adapters. I have 2 tuning adapters, one on a Series 3 and the other on the Elite, and about every 30 days I will have to cycle power on the TiVos and TAs to get the channels back. Annoying, and since this has been happening ever since TAs were released and I've tried having them replaced a few times without any improvement, I don't expect this will ever go away.
Philips Series 1 HDR212, Nov 2001, never activated (retired)
Original OLED Series 3 (Lifetime) - Nov 2006, upgraded to 1TB in 2009
Premiere Elite/XL4 (Lifetime) - Oct 2011