It would be important to determine if the problem is only in your wheel or not. Next time the wheel dies, pick up a DS4 and see if works with the game. If it does not then the problem is in the PS4; if it does then the problem is in the wheel.
That said, what you're describing is similar to a problem I'm having with my T-GT. There is a short in the wheel and occasionally (once every few days) it basically just dies. It happens most frequently when I'm racing and wind up with a lot of FFB and the wheel shakes a lot. Believe it or not, a smack up the side of the base of the wheel fixes the problem. I need to get off my butt and get it replaced with Thrustmaster, but it works 99% of the time and I love to race, so....