The thermostat is out of calibration.
If it is, the burner will be bouncing on and off. Make sure you use an ammeter when you're checking the calibration. Don't guess at that anticipator's setting.
Check, too, to see if the thermostat has a mercury switch. If it does, make sure the thermostat hangs level on the wall. And check to see if the thermostat is in a cold draft, or if it's hanging on a poorly insulated, outside wall. Make the necessary corrections.
The boiler is oversized.
You're supposed to size the boiler and fire the burner to the connected piping-and-radiation load. In the boiler manufacturer's literature, they call this load the D.O.E. Heating Capacity. If your boiler is too big, its ability to produce steam will exceed the system's ability to condense steam. The burner will short-cycle.
You may be able to solve the problem by down-firing the burner, but be careful when you try this. You may down-fire to a point where the flue gases begin to condense. Fire only to the connected load.
The boiler is properly sized, but overfired.
If there's too much fire, you'll get lots of steam in a hurry. That will quickly raise the boiler pressure and short-cycle the burner off the pressuretrol.
Raising the pressuretrol setting isn't a good solution to this problem. Over-firing will also throw water up into the piping. This leads to water hammer, uneven heating and short-cycling.
Check your gas pressure, or your nozzle size (on an oil-fired system).
The boiler is making wet steam.
Check the near-boiler piping against the manufacturer's specifications. If the piping can't separate the water from the steam, the water will cause the steam to condense, and the burner will short-cycle.
Check the boiler water's pH and its cleanliness too. You may have to clean the boiler and the system and balance the pH with chemicals.
The steam traps aren't working.
Two-pipe steam is like a ladder. Each radiator is a rung on that "ladder," and at the end of each rung you'll find a steam trap. Part of the trap's job is to keep steam from entering the no-pressure side of the ladder. If even one trap fails in the open position, steam will jump across and pressurize the air on the other side of the system. As the pressure builds, the burner will short-cycle on the pressuretrol.
Float & thermostatic and bucket traps serve the same purpose at the ends of the mains, and at the base of risers. If they fail in the open position, or, with bucket traps, if they lose their prime water, steam can move into dry return lines and cause burner short-cycling and water hammer. Trap maintenance is essential.
The air vents aren't working.
If they're not, the system will trap air and pressurize it. Remember, steam and air are both gases, but steam is lighter than air, so the two won't mix.
When the steam heads down a pipe, it pushes air ahead of itself. If the air can't get out at the end of the pipe (through a vent), the steam will just compress it. The pressure builds, and the burner shuts off on the pressuretrol. The burner short-cycles, but that's not your only problem. The building also remains cold because the radiators and mains are filled with air instead of steam. Usually, someone comes along and raises the pressure. They mean well; they're trying to solve the short-cycling and give the folks some heat. But the higher steam pressure just compresses the air a bit more. It usually doesn't help the lack-of-heat problem. It just raises the fuel bill.
Check the air vents, and clean or replace them where necessary.
The pressuretrol or the pigtail is clogged.
If there's sludge in the pressuretrol or the pigtail that connects the pressuretrol to the boiler, the burner will short-cycle. The pigtail's job is to fill with water and keep the steam temperature from reaching into the pressuretrol. A pigtail is a natural collector of sludge. If you can't clean the pigtail (a tough job), replace it.
The pressuretrol has a mercury switch and it isn't level.
Some pressuretrols have mercury switches. If the pressuretrol isn't plumb and level, the mercury might trip too soon. That can cause the burner to short-cycle.
If the pressuretrol sits on a pigtail, make sure the curved part of the pigtail faces front to back (when you're looking straight at the pressuretrol). If you have the curved part turned from side to side (so you can see through the circle when you're looking straight at the pressuretrol), the burner might short-cycle. This is because the curved part of the pigtail straightens a bit when heated. As it straightens, the pigtail tips the mercury and stops the burner. When you turn the pigtail so that it faces front to back, it tips the pressuretrol from front to back, but not from side to side. This doesn't affect the mercury switch.
The pressure is too high.
If it's a gravity-return, two-pipe system, high boiler pressure will back water up into the vents, and trap air in the system. Many of the radiators won't heat. And since air is a compressible gas (just like steam), the burner will begin to short-cycle as the steam squeezes the air into a corner. You may be tempted to increase the pressure, thinking this will cure the short-cycling. But don't do it; it will only make things worse. Instead of cranking the pressure up, crank it down. And think like air. Walk along the piping and ask yourself, If I were air, could I get out? If you can't get out, neither can the air.
Another thing: overfiring can also cause the burner to short cycle. Fire only to the connected piping and radiation load - no more and no less.
Wet steam also can cause short-cycling. The steam leaves the boiler, the pressuretrol hits its high limit, the steam rapidly condenses and causes the burner to turn back on.
Dirty water is another common cause of burner short-cycling. Clean the system with trisodium phosphate.
Want more troubleshooting tips? Check out A Pocketful of Steam Problems (With Solutions!).