I agree, his appetite is probably lacking because of the compact
UVB light. Even the Reptisun 10.0 compact/coil is inadequate for a Bearded Dragon, and if they are under inadequate
UVB light for a while, eventually it catches up with them and they lose their appetite and start becoming lethargic. And if you have a mesh lid on your tank that is blocking the compact
UVB light, he's pretty much not gotten any
UVB light, as the mesh lids block about 40% of the already too weak
UVB light.
I highly recommend that you order him a long tube
UVB light and a matching length tube fixture ASAP, as eventually the next step in this is that he starts developing Metabolic Bone Disease (MBD), which is very common with dragons under compact and coil UVB lights. I always recommend either the Reptisun 10.0 T5 High-Output UVB tube (usually the 22" is best, it comes in 16" or 22") or the Arcadia 12% T5 UVB tube. The T5 UVB tubes are the best available, cost the same as the much weaker T8 tubes on Amazon.com, and the T5 tubes only need replaced once every year and can sit on top of the mesh lids as long as the basking spot is within at least 11" of the tube, where as the T8 tubes need replaced once every 6 months, must be mounted underneath the mesh lid too, and must be within at least 6" of him to be effective.
I'd really get the
UVb light and fixture replaced as soon as you can, as this will become a much larger, more expensive issue...