It's your RCM it sounds like, search for Relay Control Module. It sends a false note to the computer when it gets hot and skews the solder, causing the computer to think there is no fuel pressure. All the electronics work but it won't start, and it can also die mid-driving just as though it ran out of fuel.

It can be resoldered at the circuit board in no time, and you're not out the $200 bucks it costs from Chrysler/Mercedes.