Why didn't Kenshin's master Hiko Seijuro fight Master Shishio? Why didn't Kenshin's master, Hiko Seijuro, come and fight Master Shishio Makoto in the showdown of the Kyoto Arc? 

This is one of the many times that the Meiji government called on Kenshin to solve their problems, even though his master is as skilled as he. (This is especially true before Kenshin learned the final technique.)
Because Master Seijuro wasn't interested! He was, to put it bluntly, an introverted, misanthropic and somewhat lazy martial artist, who thought the world an unredeemable place, felt Kenshin a fool for wanting to improve society, and didn't care in the least to take down Shishio. (See particularly his interactions with Kenshin during episode 41, "The Ultimate Technique of the Hiten-Mitsurugi Style: Reunion with a Mentor, Seijuro Hiko".) To quote from the Kenshin wiki page on him: 


  Kenshin describes his personality
  as "twisted, brusque and misanthropic" ... 
  He dislikes the complications of socialization, and hearing of the
  ills of society, both of which he finds annoying, and to the latter's
  weight, ultimately incessant and depressing. In order to avoid having
  to work with people, he makes his living as a pottery artist alone on
  a mountain (a profession that he is reported to excel at). He also
  comes off as somewhat lazy, professing to have retrained Kenshin to
  save himself the bother of having to deal with Shishio, and later on,
  he complains about having to protect Kenshin's friends, after the
  latter insists him to do so (though he does).


It's only after much cajoling that he agrees to teach Kenshin what he needs to know to defeat Shishio (episode 43, "Between Life and Death: Master the Ultimate Technique, Amakakeru Ryu no Hikameki!"), but beyond that, the most he will agree to do is to (grudgingly) keep an eye on and protect his friends, while Kenshin does the actual hard work of fighting Shishio (episode 53, "The Giant Versus Superman: Like an Arrow Shot at a Time of Despair")!