You either have not enough air in the pressure tank or just not enough pressure tank - normally recommended to have enough capacity so the pump runs for at least a minute or two to refill it. One way to get an idea is to measure the volume of water that is drawn when you go from 55 to 30 PSI and compare it to a chart for your tank, or a tank of the same size. Using this pump calculator for a bladder type tank and your cut-in/cut out pressures, you should get about 7 gallons from a 20 gallon tank. If you get much less, you have an issue.
Another is to completely drain the water from the tank, and check the air pressure - if it's a bladder-type tank, it should typically have 28 PSI or so for a 30-lb cut in pressure. If the bladder is burst, it may have no pressure when drained. If it's a non-bladder type tank the explanation of how to maintain antique finicky things gets complex. I'd suggest replacing one with a bladder tank, and IME the same applies for a burst bladder (replacement bladder was most of the cost of a new tank, and the new tank came with a 5-year warranty, while the replacement bladder came with none. YMMV.)
If it's able to keep refilling the tank to 55PSI while you are using the hose, there's probably enough flow. If it's not merely a problem of insufficient pressure in an intact bladder tank, you can either replace a broken tank, add tank capacity, or try a "constant pressure valve" retrofit - essentially a leaky pressure regulator, where the tank would drop from 55 to 30 (unless adjusted to a different cut-in/cut-out), make its way back up to 45-50 or so and stay there as long as you were using water, and then rise to 55 (unless adjusted to a different cut-in/cut-out) and shut off when you stop using water. They claim you can use very small pressure tanks with them...
You can also reduce the extent to which you see pressure change at the hose by using a pressure regulator ($6 or so) on the hose, so that the hose only gets 25 or 30 PSI regardless of the pressure in the well tank, but that's an approach for after you sort out if your well system is working correctly.