Long as your pump is getting oil, it will work. A bit of air in a cylinder versus a minimum of 1500 lbs of hydraulic pressure....air looses. Drain the oil out of the tank, check the screen in the tank, clean if required, reassemble. If desired the supply line to the pump could be removed and a pan placed under it, dump a couple of gallons of oil in the reservoir and see how fast it runs out. It's never happened to us, but I've heard of supply hoses collapsing internally and cutting off the flow of oil, have also heard of fuel supply hoses doing this.
I'm no expert either but I do repair almost all the hydraulics on the farm and have even worked on some hydrostats which can carry up to 5500lbs of pressure, if the pump is getting oil, it will displace the air.
Me thinks something else is causing the pump not to get any oil. Could even be as perverse as the key has sheared on the shaft that drives the internal pump gears. I've had this happen on spray pumps, shaft turns, even moves fluid till x amount of pressure is obtained then they fall flat on their faces and nothing happens.