Why didn't Rayleigh try to save Ace? - One Piece

The only reason I can think of is that Rayleigh had no idea Ace was Gol D. Roger's son. The entire world knew him as Fire Fist Ace, the infamous pirate who was the 2nd Division Commander of the Whitebeard Pirates. There was no information about his past.     

As you can recall it was the former Fleet Admiral Sengoku who revealed that Ace's father was Roger just before the execution was supposed to begin. Before that it was only Garp,   

 Luffy and maybe the admirals who knew the truth about Ace. And maybe Rayleigh came to watch the war after Sengoku reveal Ace father.       

In the flashback it was shown that Roger stayed hidden for a year after disbanding his pirate crew. It is possible that not even Rayleigh knew where he was or with whom he was and that he was expecting a child. The only person with the information about Portagas D. Rogue was Vice Admiral Garp.    

No one could suspect the navy hero to be raising the child of the Pirate King as his grandson.  Ofcourse if Rayleigh had any idea he would have been there to fight alongside Whitebeard.