Air stuck in central heating system

[ZeroTools]

I have air stuck in my hot water system which is characterised by a loud humming/vibrating noise coming from my hot water pump every 10-15 mins for about 3-4 mins at a time (presumeably as the pocket of air cycles around the system and hits the pump). I have tried bleeding all the radiators in the house that I can (some wont as the bleed valves are seized), I've tried bleeding the pump when it is making the worst noise, and I've tried bleeding the valve at the cyclinder. In all cases I get zero air out. The entire system was drained down and refilled, which fixed the issue for about a week, then one day I came home and found a low pressure error on my boiler. Back round I went, bleeding everything again. I managed to get a little air off a towel radiator and some from the valve at the cylinder, which was enough to get the boiler to fire again, but I could hear the whistling as it pumped air before getting some hot water through. Now I'm back to square one again. I would love some advice on how to clear this for good!