Gravity -fed airbrush

First, you have a siphone feed AB.  Second, the problem you mention is caused by the following.
1. Inadequate air pressure <-- Check your compressor psi and blow air thru your AB without attaching a jar. How is the air flow? For a siphon feed AB, the minimum is 16-18 psi.

2. A tiny air hole of the jar lid is blocked.

Sounds to me like you have a siphon fed airbrush (gravity fed has the paint reservoir on the top or possibly on the side). I don't know which AB you have but your problem could be as simple as making certain the small bleed hole in the bottle cap is not clogged with paint or other stuff. Or it could be the nozzle if it isn't properly seated. If your AB is otherwise very clean, I'd suspect the little bleed hole in the lid of the paint jar/bottle -the bleed hole is very small so stick a pin through it to make sure it's open.

Sounds to me like a blockage some where. I know it might seem an obvious one, but have you stripped them down and given a proper clean.