Hello, just to confirm, are you saying the engine stalls out when under a hard load, as in RPM's begin to drop? If yes, it's most likely a fuel delivery problem. It's a little tougher to troubleshoot when the engine is just slightly stalling, and recovers quickly when the load is released. It's a little easier to figure out when it get so bad that the engine dies.
Two very common causes with Bobcat machines with this problem is 1) strainer on the end of the pick up tube inside the tank is getting clogged by debris in the tank, and 2) pick up tube inside the tank is broken off where it connects to the elbow fitting at the top of the tank. With the latter, when the pick up tube breaks off, it will run relatively fine with a full tank but begins to labor to run, even dies, when the fuel level drops, doesn't really sound like your problem. The other cause, strainer on end of pick up tube clogged by debris, typically causes the engine to stall when under hard load, when much fuel is demanded but it can't be delivered because of the restriction.
The easiest way to confirm pick up tube strainer clog is the primer bulb. If it's good and flexible, not hard as a rock from age, if you can keep pushing the machine hard under load and actually make the engine stall and die, quickly jump out of the cab and fling open the rear door, check to see if the primer bulb is sucked flat. If yes, strainer is clogged.
Of course there are other engine components that could cause this problem, failing lift pump for example, but the most common cause is a problem with the pick up tube or strainer. If I can't confirm the pick up tube or strainer is the problem for sure, before I start replacing other components, I always go to the pick up tube first, pull it out and inspect it, even though it's a PITA to do, it's just that common. Let me know what you find.