How to approach absolute pitch recognition: compare to the remembered reference (or a root sound from a song) or to assign a special pitch quality to the note? I can recognize several pitches, but do mistakes sometimes when testing hearing with softwares. With age, perhaps, I am losing my hearing and pitch recognition sensitivity.
Well, David Lucas Burge developed a method that he sells to give anyone perfect pitch. A friend of mine tried and it helped him a lot. Basically it helps you associate colors to every note to make them each individual. And many others, him included I think, tell you to also associate music pieces to various notes or tonalities.
I tried many of these and get it right 20% and wrong 80% of the time so I must be a bad student :-( But it works for others!
Absolute pitch recognition may be impressive if only because so few people can do it. However, relative pitch recognition is much more useful if one is to translate and reproduce sounds with any sort of efficiency. It's the relationship of sounds to each other--linearly (melody) and accumulatively (chordal) that is the essence of music.
Another way to look at this, from my point of view, is: What you get out of relative pitch recognition is the relationship of sounds. What you get out of absolute pitch recognition is a classification of sounds.
Another way to understand this is to think of color recognition. Absolute color recognition allows you to (think you can) accurately name a particular color (a philosophical impossibility? -- see Wittgenstein). Relative color recognition allows you to accurately generate a spectrum of colors.
There's not much evidence that true absolute pitch is learnable at all, much less supporting one learning approach over another. (See e.g. https://en.wikipedia.org/wiki/Absolute_pitch which claims "there are no reported cases of an adult obtaining absolute pitch ability through musical training".)
You may want to think more about what specifically your goals are other than just absolute pitch for its own sake.
This is based on what I learnt at school many years ago.
If you were asked to sing a note (Middle C for example) and you do not have perfect pitch then the best you could do is guess where you "feel" it to be. However, if you were asked to sing a Middle C a few seconds after it had been played to you on a keyboard then you would most probably be able to do it. Why is that? It is because you have remembered the pitch. Twenty minutes or two hours later you may not be able to recall it, so short-term you can remember but long-term is more difficult.
What you are trying to acquire is a memory for pitch. You already have that as a short term ability, what you need to do is develop it as a long term ability.
If learning to recognize pitch is possible then I would expect that you would have to practice.
So why not practice? Every time you pass a keyboard try to guess Middle C and then check to see if you got it right. When they announce a piece on the radio and you know what note it starts with try to guess it before it starts. I don't know if this would work but it might be worth a try for a few weeks to see if you can improve your abilities.