It's a good point about the detergent.If a beer's carbonated, even to a low level, it should keep a head. Have you thought about your glass? The slightest remnant of detergent will destroy the head. If that doesn't fix it then stop wearing lipstick while drinking beer.
Talking of beer glasses, it reminds me that the other day we were sitting in my friend's back garden sampling my pilsner. When poured all the beers had a decent head, but we noticed that it was lasting much longer in one glass (a 'proper' Belgian beer glass) than it was in the others. Looking closely, we realised this was because it had a sharp pointed 'star' design etched in the bottom of the glass. This was acting as a nucleation centre, and creating steady stream of bubbles which kept the head topped from below. Interesting!
I looked this up and it's definitely a 'thing': What is the purpose of an etched glass?
Edit: I checked my beer glasses and found something similar in the base of this 'Chimay' one:
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