Think of it this way. A strong acid in the BL model is something that very willingly gives up a proton, while a strong base is one that very willingly accepts a proton. If it really wants to give up the proton, why would the resulting compound want it back? If you look at the resulting structures there is usually some relatively electronegative molecule/atom that is very stable with the negative charge, stable enough that a proton is much less likely to be added back.
Answers & Comments
Explanation:
Think of it this way. A strong acid in the BL model is something that very willingly gives up a proton, while a strong base is one that very willingly accepts a proton. If it really wants to give up the proton, why would the resulting compound want it back? If you look at the resulting structures there is usually some relatively electronegative molecule/atom that is very stable with the negative charge, stable enough that a proton is much less likely to be added back.