Step 1: What the reaction needs.
In this addition, the nitrogen of ammonia (or one of its derivatives) must act as a nucleophile. It uses its lone pair of electrons to attack the carbonyl carbon. So a free, available lone pair on nitrogen is essential.
Step 2: What strong acid does to the reagent.
In a strongly acidic medium there are plenty of \(H^+\) ions. These protonate the nitrogen of ammonia or its derivative, forming a positively charged ion like \(R-NH_3^+\).
Step 3: Effect of protonation.
Once nitrogen is protonated, its lone pair is used up in bonding to the proton. With no free lone pair, the nitrogen can no longer act as a nucleophile and cannot attack the carbonyl carbon.
Step 4: The opposite extreme.
If the medium were strongly basic, the carbonyl carbon would be attacked easily, but then protonation of the intermediate (needed to lose water) would not happen well. So the reaction needs a balance.
Step 5: The right condition.
A weakly acidic medium (about pH 3.5 to 4.5) is ideal: it is acidic enough to help the later steps but not so acidic that all the nitrogen gets protonated.
Answer: In a strongly acidic medium the ammonia derivative gets protonated, so the nitrogen loses its free lone pair and can no longer act as a nucleophile to attack the carbonyl carbon. Hence nucleophilic addition does not occur; a weakly acidic medium is needed instead.