I have a 3 wire grounded Romex cable connected to 2 circuit breakers by sending one black to a breaker and one red to another circuit breaker. They lead back to the kitchen wall where one gives power to the garbage disposal and the other gives power to the dishwasher. Both have GFCI protectors on the circuits. THey have worked well for 8 years.

Problem now is that I have lost power to the dishwasher without tripping a circuit breaker.
When I turned off the garbage disposal circuit, the dishwasher circuit became hot and worked normally. I suspect a short circuit but no circuit breakers have been tripped.
How can I trace back to the point of the fault and repair it?

A 12-3 has 4 conductors(red,black white and green.)
Something has opened, breaker may have tripped but not thrown.
A Meter will be necessary to follow the circuit.

The plug for these uints are under your sink? If so turn the power off to both the g/d and dishwasher,test for power coming from both halfs of the receptacle. How, plug a radio into each side make sure the radio is on when you go under the sink, open the receptacle and remove it from the wall take a good look at it you will see tha the white wire is on one side and the red and black are on the other side you will notice that the white wire side has a tab between the top and bottom while the red and black side has been cut out ,this is to separate the two hot wires and create two circuits. You should have noticed if the wires are loose by now push on the wires then tug them a little to make sure they are tightin the receptacle, if screws are used tighten them up. Replace the receptacle if you have to be sure to cut or break the center tab on the hot side.This should fix your problem if not you will have to go into your panel to tighten the wires on the neutral bar and circuit breakers do not do this if you are not comfortable working on electrical equipment!!