Hi all. I am a heating engineer in Boston and teach a workshop at my local building materials co-operative. The issue you describe comes up as an FAQ more than any other.
All the talk of venting, and how it is an annual ritual ignored the problem but treats the symptom only.
The only time you should ever need to put new water in your system is at inital filling and upon repairs if any. New water = new oxygen. Where is the air coming from? Not (directly) from the atmosphere! You heating system runs at between 12 and 25 psi guage pressure (atmosphere being zero guage). Air simply will not leak towrds higher pressure. My experience:the old expansion tanks, ideally half-filled with water, half air, as a cushion to absorb thermal expansion. That is the only air in the system. Solution? "Diaphragm" or "bladder" tanks, where the gaseous cushion (air or nitrogen) is sealed from the water. Replace the old tank with these and you will not have to vent again.
Cost? About $50-65 per tank. I recommend two in battery, should one fail. Also, size these based on system water volume NOT system btu rating which applies to small tube copper (low volume) baseboard systems. Manufacturers?-Taco, Amtrol, Vent-Rite, Armstrong, to name a few. "Teel" is a Grainger line also.
Once filled and vented- heat the water up and circulate for a few hours or a couple of days to drive the air out of solution -you are done!
Another nice touch: an air separator, not the cast iron scoops we all have seen, but a real one such as Spirovent. One pass removes 90% of air from even cold water.
One last item- I am often asked how much pressure to fill a system with to initially. Generally, you want 4 psi pressure at the top, to force out the air, and to prevent draw-down (vacuum lock) when the pump runs. To figure pressure, measure from top of the highest radiator down to the boiler pressure guage, in feet. Divide by 2.31 which is the height of a column of water that yields one pound per square inch (psi) pressure. Say you have 25 feet of height. Divide by 2.31 =10.82 psi +4 psi =14.82 psi. Call it 15 pounds, cold fill.