It is unusual for juveniles to brumate as they usually don't have the reserves necessary to decrease calorie consumption. It is not unusual for beardies to have definite food preferences and for young dragons to decline veggie foods in favor of live prey. Sometimes if you put the live food in the salad bowl it will induce an accidental bite of salad.
First, the obvious basic questions. Are his temps high enough in the basking zone (100-110 F)? Are the lights bright enough and does he get sufficient UV exposure? Is he on sand or other particulate substrate (Can irritate eyes and digestive tract)?
Has he every been evaluated or treated for parasites? Even a vet unfamiliar with reptiles can run a fecal screening. Does he get a vitamin/mineral supplement with his food? Live prey should be dusted with a good supplement daily. What veggies are you offering? How often is he fed live prey?
Some basic recommendations: First, get a fecal screening. If it comes back positive, you will need the appropriate treatment for the parasite(s). Second, hydrate him well by soaking him in warm (not hot) water several times a day. You can also drip fluids on his nose during the soak (Not all dragons can be bothered to recognize standing water, even while immersed in it). Very gently cleanse his eyes with moistened cotton swabs while he's in there. Does he have any nasal discharge? Wheezing while breathing? Gaping or gasping while inhaling or exhaling? He may have a respiratory infection. An infection will also decrease the appetite. When his eyes are cleaned do you continue to see any discharge being extruded? Do you see any scratches or injury to the eyes? Up the temps a bit in the basking area and add a bit of belly heat for night and day warmth if you don't already use an undertank heater. Make sure his diet and supplementation and environment are optimal. Good luck!