The threat against the Watsons meant Sherlock had no time
At the same meeting that Moriarty revealed his disposal of Irene Adler, he issued a direct threat against John and Mary Watson, which was carried out quickly - note the overwhelming force deployed in the train sequence. Sherlock safeguards Mary by placing her with Mycroft, and John by recruiting him for one final mission. Until Moriarty is conclusively defeated, the Watsons are in terrible and present danger. That cannot wait for Sherlock to investigate the fate of Irene Adler.
Sherlock seems to have accepted Irene's fate
In a quiet moment on the ferry, Sherlock inhales deeply from Irene's bloodstained handkerchief and then throws it overboard. His disinclination to retain possession of such a clue suggests that he has accepted that there is little he can do to help Irene Adler now.
