Cruise control on 2004 Jeep Grand Cherokee Limited works periodically - once you step on the brakes it will not work again until it is shut down and restarted (sometimes not even than -is it a vacuum line issue or something else?
First, once it has set and held the speed, and then won't reset after tapping the brake pedal, hold the pedal up with your toes, then see if it will resume. If it does, suspect the brake light switch adjustment or the switch itself.
The next plan is to visit the Chrysler dealer. Right around 2004 is when they were switching over to the more complicated electrical systems so I don't know which scanner they will need. The older version has a screen for "last cruise control cutout". The mechanic will need to drive the vehicle until the problem occurs. I think the newer version has a "mini scanner" that you can take with you but if that is correct, I never used one myself.
Since you stopped at the shop to have the repair order written up, the latest reason for the cruise cutout will be listed as "ignition switch turned off". Sounds obvious, but there's a reason for that. If you were to leave the engine running while the mechanic connected the scanner, the reason listed would be "vehicle speed below minimum threshold". It won't engage below 35 mph.
What you need to do is drive it on the highway, then read the reason when it won't resume. This is more useful when the cruise cuts out on its own while driving. If the reason listed is "brake light switch applied", the brake pedal was vibrating over bumpy roads and the switch is misadjusted. If the ignition switch was listed as turned off while you were driving, you would look for a loose electrical connection or something related in that circuit.
In your case where you know it cuts out from hitting the brake pedal but it won't resume, the scanner will also show the state for all of the switches. If it shows "brake switch: released" and "ignition switch: on", you might find "resume switch: released" even though you are pressing it. That would point you to the switch assembly or the wiring which includes the clock spring under the steering wheel. That's a wound-up ribbon cable in a plastic housing.
Between the "reason for last cutout" and the switch state screen, those will get you to the right circuit to troubleshoot.