Not always to do with AT.
For instance I may be at a modern jive dance and a track comes on that has a chachacha beat and I do not recognise that.
I also find it very difficult to hit the breaks in general swing music.
In both AT and other dance where there is a track and they may drop the up beat so it is silent that would throw me.
Where in AT they change the beats in a phrase randomly (Biagi in particular) that throws me.
I cannot always tell what instument is playing, I am particularly unsure about when the bandoneon is playing.
I am just beginning to understand both in my head and my ears syncopation. For instance I am now beginning to pick up the use of syncopating the 2 beat in dance terms. Whether delaying or accelerating. However I am still having trouble understanding what is meant by 3,3,2 syncopation.
In general terms I still need to educate my ears more. When I go to talks on music they point out so many things to me that I would not have noticed. I am beginning to hear more in the msuic than I used to. I suppose I want a way of using the deliberate practise methodology in another current thread to improve things.
OK, so rhythm is an area to work on.
The beat is often not obvious in tango music and I can relate to your problem. Often a regular pulsing sensation is missing. The beat is still there, because music moves at a regular pace through time. (Almost always for the type of music we are talkng about). Listen to some music you are having trouble hearing - Biagi. Count and/or tap the beat continuously and regularly. The beat may be slower than you are hearing it. If the music sounds fast it is because the beat is being subdivided into smaller time values. (Recall eighth and sixteenth time values?). You will eventualy be able to hear and feel the beat even when it is hidden.
Take a look at this demo of tango rhythms
http://www.youtube.com/watch?v=Uxi7WFlQAf0
Deliberate practice requires a teacher to instruct and correct errors. I can suggest some simple drills, the rest is up to you...
Use this on-line metronome
http://www.metronomeonline.com/
Click on 70bpm (make sure your speakers are turned on). That will be the beat. Do the drills with different tempi (bpm) too.
Either think in 2/4 or 4/4. It doesn't matter - try both.
In 4/4 time signature there are four beats per bar.
In 2/4 time signature there are two beats per bar.
Some exercises in 4/4 (you can adapt for 2/4):
Count (in your head) and tap quarter notes (one per beat) along with the metronome 1 2 3 4, 1 2 3 4...
Count and tap eighth notes, there are two for every beat of the metronome: think 1&2&3&4& 1&2&3&4&...
Count and tap sixteenth notes, there are four for every beat of the metronome: think 1234 2234 3234 4234..
Count and tap a pattern of 2 eighths, 1 quarter, two eights, 1 quarter: 1&2 3&4, 1&2 3&4...
Count and tap four sixteenth notes, two eighths, 2 quarters: 1234 2& 3 4
Devise various drills yourself, using different combinations of note values.
Some more difficult drills:
Let's switch to 2/4. Use the metronome.
Count and tap continuos sixteenth notes: 1234 1234, 1234 1234...
Now count every sixteenth note but tap only on 1 and 4
Still counting countinuous sixteenths, tap on 1, 4 of beat one then tap 2 eighths on beat 2 (habanera rhythm)
Still counting countinuous sixteenths, tap on 1 and 2 and 4 of beat one then tap 2 eighths on beat 2 (A habanera variation)
When musicians are first starting out they are taught to do these sort of rhythm drills. Then music is put in front of them and they tap the rhythms. Eventualy the teacher will clap rhythms and the student has to clap them back - no music just ears. The rhythms start simply and eventualy they get quite complex.
There are several music syllabi with international recognition. The Royal Conservaotry of Music in Canada, and The Associated Board of the Royal Schools of Music in the UK are two. There are published course materials and workbooks available, very methodical and well presented.
And maybe take some lessons from a music teacher.