When Sauron surrendered to Ar-Pharazon and was taken prisoner to Numenor, did he take the Ring with him? If he did it seems unlikely that the King would allow him to retain such a powerful artifact. (He wanted to control the entire world, and it certainly would have come in handy when he invaded Valinor!) Also, when Numenor was destroyed his body went down into the chasm with it. Only his spirit survived. If he couldn't save his body, it seems unlikely he would have the power to transport any material object like the Ring.
However, if he left the Ring in Middle Earth, somebody had to be in charge of it for the 57 years Sauron was in Numenor. But who could Sauron trust to this extent? If the Ring was left with someone of little power who would be unable to wield it, then someone of greater power would be able to take it away from him. If it was left with someone of potency (to continue the banter above), then the Ring would surely tempt him to grab for supreme power.