That is a private label Astro 135, good gun. Not the most powerful (IIRC ~80ft/lb), but fast and durable.
It is a rocking dog clutch. When you turn the anvil, the clutch engages and it stops, likely the problem is in the air motor, broken vane, bad bearing, stuck from rust, etc.
To take it apart; put the anvil against the bench and push on the handle housing, the anvil should push in and air motor end start to come out. Hold the air motor in and turn it over so the anvil is up (I prefer to put the cover back on so the parts stack on it). Using a tool (punch, etc) push down on the anvil and pull up on the housing, the housing should pull off. The air motor should be a slide fit, but sometimes requires some persuasion, if so, be careful with alignment, it needs to come straight out, if it becomes cocked will be much more difficult. If tight, best bet is to apply some oil, push it back in, repeat until it comes out smoothly.
Once it is out, the impact clutch just connects with splines, so can be lifted off and set aside. The air motor front end plate should lift off, then the cylinder. Now should be able to see the problem, is a vane broken, stuck, they should move smoothly, rust, bearings turn smoothly, etc? Shoot, post pix.