I have been running this projection TV for several months in conjunction with an Onkyo receiver. Cable and DVD players work fine. This week my son is visiting so we powered up the PS4 for the first time. (I am not a gamer) The PS4 also is wired into the receiver. It works great for ten minutes at a time, then the BenQ TV powers down on its own accord. I fire it back up, it works for another 10 minutes, then powers off.
ETA: "Power" and "temp" lights are on.
ETA 2:  This occurs only when gaming.  Standard DVDs play fine in PS4 without timing out. Will try with Blu Ray later today. ETA3 : Blu Ray worked fine as well. Went to lower resolution in game mode. Lowest setting. It now goes 20 mins before timing out.
ETA 4 Timed out 1 hour into a Netflix movie last night.
Contacted customer support. I have to send it in for evaluation and repair. Failing heat sensor is suspected.
They say they will try to cover under warranty.  Bought in July 2015, not installed until June 2016, unit has well less than 100 hours. If not warranty, I am probably looking at around $150 to fix.

Currently rethinking my choice of BenQ. We will see how it works out and I will post results so others may learn.

Final update: Projector back in about a week and fixed under warranty.  I am out $50 in shipping even though BenQ sent me a prepaid FedEx label, but for some reason I got the label 5 days after they sent me the RMA number.  I had already shipped it back on my dime.  So far it seems to be working properly.