I've had this old Coats manual tire changer for years, use it often. The cylinder leaked air when I got it but it still worked. Now the leak is worse and enough air is leaking that it won't break the bottom bead. Anyone ever taken apart and repaired one of these air cylinders? I think it's the "All Star 605" model.
I took the one apart on my newer tire machine, I had to clean up the cylinder and coated the seal with grease. put it back together and it has been working ever since.
Once you fix it up, keep the exposed part of the ram and above where it comes out, packed with grease.
I don't see any springs in your picture to pull the arm down and if that is a single acting cylinder there could possibly be a spring inside. In that case, I'd put it in a press while removing the snap ring. Also look at the outer lip on the snap ring groove, many times a cylinder that has been in use for a long time ends up with a ridge on the edge that will catch on the cylinder head when trying to pull it. After removing the snap ring, we used a burr in a drill to remove the ridge.
You might start with the hoses, clamps, and fittings to see if that solves anything. I've had spilts on hoses hidden inside the wormdrive clamps that were impossible to detect unless they were removed completely and inspected.
I see you have it bolted to a steel grate, good idea will have to try that with mine that's buried in the corner.
Leaving it outside probably let the cylinder rust. A good cleaning may help, McMaster Carr has all kinds of seals.
I've seen...not done, many pneumatic cylinders being rebuilt. They were used as brake actuators on large winches. Most of them are super simple and similar to hydraulic cylinders, kind of like a tire pump inside. Usually they had problems with worn shaft bushings or water rusting the cylinder, with the rust wiping out the air seal. I was surprised to find many of the seals were just one or more large o-rings set in a grooved disk. They'd replace the bushings, hone the cylinder and roll off a piece of the right diameter o-ring material from a roll, cut the ends at an angle and super glue it together.