At this point after 6 years you know the Contax.
But just a few suggestions.
Did you try a different lens, prism, do you have an extra body?
If not and the kit you have is one lens, one body, one back, take the camera apart, (be very careful with the shutter curtain as on the Contax it's very easy to punch your thumb through it.
Look to see if anything is amiss. Like the shutter curtain, mirror, check the lens to see if it stops down. (Actually try a few frames with available light and see if the shutter works, the lens stops down throughout the range.)
Also put in fresh, new batteries and if you tether try the camera tethered and un tethered to a cf card.
If you have the 90 degree grip, only use the AA batteries to get you through a session, then at your first break put in a new 2cr5 battery in the vertical part of the grip.
The 2cr5 battery should always be your main power source.
Then disassemble the camera, take a lint free polishing cloth, and polish every contact on the Contax. Prism, lens, body, (both ends) and back.
The one downside of the contax is every contact point has to be secure as they work in sync. The prism only partly connected will throw everything off.
When you polish the contacts, do it like your polishing a jewel, making sure they are complete clean and shiny and once you think you've got it, do it again.
Another weak point of the contax is the prism mounting brackets. They're made of some kind of composite material and easily crack if the camera is transported with the prism on or if you lift the camera with force by the prism.
It's hard to see the cracks, but a way of check this is to mount the camera on a tripod, set up your flash sync, and when you fire firmly press down on the front center of the prism to make sure it's making contact.
Everything I've mentioned I learned the hard way. One on high pressured shoot, I couldn't get the 140mm lens to work, just wouldn't fire with regularity. Luckily the studio had one in rental and I bought it, thinking my lens was down.
Turned out all the lens needed was a good polishing of the contacts.
You might have more serious issues, than what I've outlined and It may seem like I'm making the contax look vulnerable, though I've shot a trillion frames with my contax' and never had one go down, other than the contact cleaning and the prism clips got cracked, but other than that I'd be totally shocked if a P series back or the contax actually broke, though I guess anything can break.
I actually think the Contax is the best medium format camera ever made for digital.
Good luck.
BC