This is one of those cases of more data needed. Headsets that mysteriously loosen despite tightening, usually have worn cups and bearings and need to be replaced. Small wear in the crown race can also result in loosening. But the usual case is that there is a tiny bit of play at different fork rotations that will indicate this kind of wear and you're likely to sense that when stopping. So the question is, do you have play in the head set when adjusted properly if you turn the steering left/right and try to rock the fork with front brake applied?

If you don't have play, do you have hints of "indexed" steering when you have the bike in a stand with no additional force on the front steering? If you do, then you probably have to replace the headset.

With older bikes, I've had reasonable success with Tange Passage headsets. They have seals, and use regular balls and are a low as $10 a set and come in 26.4 and 27.0 crown race. I like the low-end Ritchey headset as well which is about $20, but it's a 26.4 crown race only. I don't have a current source for 27.0 Ritchey compatible races so it may only work on older bikes with 26.4 crown race. If you don't know yours, you can remove the crown race and it's sometimes stamped on the underside. Or get some really good calipers.