Master Yoda survived Order 66. Sidious was surprised Yoda survived, he did not expect it. They fought their dual and Sidious clearly won the dual, but did he really think Yoda was dead. At the same time on Mustafar, Obi-wan was battling Anakin. This dual was won by Obi-wan. Sidious must have known that Yoda and Obi-wan were still alive, yet he did not use his Clone army to search every single planet known at that time. Had he ordered an extensive search of every system in his empire, he would have found them.

I think there is an reasonable explanation for this.
I believe Sidious did in fact order a search for the missing Jedi, most of the other Jedi that survived Order 66 turned up and died. At this point it would be reasonable to think Yoda and Obi-wan were dead, and call of the search.
During the first years of his rule Sidious had other things to worry about than two missing Jedi. You must realize that declaring himself Emperor did not give him control over all planets in the galaxy. In these first years there were multiple planets that tried to stay out side the empire, these planets were "corrected" as soon as they showed any signs of hostility towards The Empire. Anyone who did not join the empire was forced to join them.

Example:
There were planets, like Naboo, that tried to remain independent by negotiating with The Empire. When diplomacy failed Naboo started exploring military options, at this moment The 501st Legion was ordered to perform a radical destabilization of Naboo's government. This meant that the government of Naboo would be decapitated by killing The Queen and anyone who was loyal to her.
The Queen of Naboo was killed and Naboo's new government was loyal to the Empire.
Problem solved.

The Emperor needed his army to concentrate on protecting the Empire from treads that he considered to be more important than two Jedi that might already be dead. Two Jedi were hardly enough to overthrow him, the real treat came from disobedient planets and The Rebel Alliance. He did not know about the twins, if he had know he would have done everything in his power to find the twins and the Jedi.
Yoda knew this was not the time to challenge the Emperors Power, he knew he had to wait until Luke was old enough to be trained. He knew the Emperor underestimated The Jedi's ability to overthrow him. Yoda and Obi-wan waited patiently for Luke's time to come.

The Jedi survived because the Emperor did not consider them a threat, he made a mistake and it cost him has empire and has life.


All comments are welcome
Remember, The Force Will Be With You..........Always.