What other symptoms?
Power indicator on? If not, check things that affect power, like circuit breakers (things that reset, obviously not fuses).
Does it consistently take the same amount of time to shut down?
Can you affect the amount of time to shut down by removing heat (removing case, or routing an air source into the receiver)? If so, you can selectively spray a cold source (used to be trichlorotrifluoroethene - outlawed, so go to Radio Shack for current troubleshooting aid) on internal areas to see if the receiver will reactivate. If successful, start isolating to smaller and smaller areas, until offending component is found.
I'd have to look at it to provide help beyond this. Unless you have experience, your chances of success are small. A good technician is worth the money. I'm a EE, and been troubleshooting for nearly 40 years.