Wow, this thread has derailed.
The OP asked why the .38 Special had fallen out of favor, and we've wound up talking about the infamous FBI Miami shootout.
Interestingly, as already by noted by several members here, the FBI's own investigation revealed that it was a .38 Special round that finally ended that fight. The FBI Miami shootout post incident investigation didn't indict the .38 Special FBI Load (+P 158gr LSWCHP) form. That investigation did indict the performance of their 9mm Auto cartridges, and lead to the FBI's adoption of 10mm Auto, which itself subsequently lead to the development of the .40 S&W round.
So, the FBI Miami shootout confirmed that .38 Special is effective, and didn't lead to it falling out of favor. Now, let's try to answer the question of what has lead to the round in question falling out of favor.