It won't matter much to the end result, but... you've posted in the 360 board but have referred to a TiVo. They're completely different boxes, so can you confirm which you have? If you're not sure, check here . If forum staff pick this thread up, it'll certainly help to be sure.
Regardless of the answer, a box that's rebooting itself is faulty - it shouldn't be happening. You can report box faults by calling VM on the usual number (150 from a Virgin phone, or 0345 4541111 from any other phone), or by waiting on here for VM staff to pick it up.
The latter may take a day or so, and it will certainly help if you can confirm the box you have.
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Our box is just a normal Tivo box and it just keeps switching itself off, it as been doing it a while now. I have tried contacting virgin by phone but it is a waist of time as you can`t get through and even on chat it takes ages for someone to acknowledge you. When it switches off all the lights flash and it takes ages for it to come back on