The PS4 isn't going down. It's only my wife's phone that cuts out when the PS4 is on.
It's not the number of connections. Like I said, I've had my PC, my laptop, and my phone all going while the PS4 is on, and haven't had any issues. My wife's phone is the only thing that cuts out when the PS4 comes on. Even if it's only the PS4 and her phone and no other devices.