The reg/mt you pictured does have the drain valve, having a little moisture in the trap is okay, it shows that it is working. If you are getting debris through your airbrush then it is coming from something after the moisture trap. Your hose may have decay or been pinched and cracked the rubber lining.
You said you were not using a tank, so rust from the compressor itself is a possibility but it too should be caught by the moisture trap. If your compressor is a sliding vane type the blades inside could be damaged and beginning to deteriorate. Piston type compressors need lubrication from time to time.
If moisture is a constant issue, then where the compressor is located is a high humidity area. You may not think so but when a compressor does its thing, it is squeezing air through the trap separating it from the air. Hence your trap fills up.
Another thing I do with my compressor w/tank is add some alcohol to the tank and to pick up as much moisture as possible. I drain it often. I run the compressor with the bleeder valves open for a few minutes each month to flush the system out.
I use to design and work with compressor systems that are as large or larger than most folks living rooms. Given the volume of air a hobby compressor moves the moisture trap filter should last a long long time if you have no tank. If you are using a tank, then it could become contaminated with rust from the tank or debris from the compressor itself.
You may want to run a dehumidifier in your workshop to keep your humidity at a level around 40-60%. Pick up a humidity gauge at your local hardware store. I have a digital one which works very well and it was about $20.
Oh, if the moisture trap isn't assembled correctly it will allow water to pass. Usually it is simply an o-ring not in its proper place.