What exactly do we mean when we use term titratable acid in renal physiology? Why is ammonium not considered a titratable acid?
Titratable acidity is a total amount of acid in the solution as determined by the titration using a standard solution of sodium hydroxide (titrant). In other words, it is the maximal capacity of the solution to "neutralise" base solution.
H$^+$ produced from CO$_2$ and H$_2$O is actively transported into the distal tubular lumen. Titratable acidity is the amount of the H+ which is buffered by bases present in the tubular lumen. Mostly by phosphate (the highest concentration).
When the urinary pH change other molecules can gain the ability to buffer H$^+$. For example creatinine (pKa about 5.0) or ketoacids (pKa about 4.8) may contribute to the titratable acidity.
Standard measurement of the titratable acidity with the standard solution of sodium hydroxide spans pH range up to 7.4. Therefore:
Ammonium is not measured as part of the titratable acidity because the high pK of ammonium means no H$^+$ is removed from NH4$^+$ during titration to a pH of 7.4.
I am answering more to the second part of your question as to why Ammonium is not considered a titrable acid.
The pKa of Ammonium is approximately 9.25.
By definition the titrable acidity of a solution is the amount of base (NaOH) that is required to neutralize the solution. On being neutralised the pH of the solution becomes 7 (neutral pH). For neutralisation to happen, the hydrogen ion(H+) from the acid should react with the hydroxyl ion (OH-) of the base to form water (H2O). For this to happen, the acid should be in its dissociated form.
However the pKa of Ammonium is higher than the neutral pH. It would mean that at a pH of 7 (which is the end point of titration) Ammonium ion still retains its hydrogen ion (H+), thus its contribution to the titrable acidity of the solution is minimal, if any.
This is why Ammonium is not considered a titrable acid