Please post a raw file that produces your problem. Otherwise you will not get at the source of the problem. It is apparent that your skies are suffering artifact. The question is,"why?"
If your artifact occurs because you edit the image too far beyond what the destination output space and format can contain, then saving is not the culprit. Converting from your working space to the output space can also affect the way blue gets remapped during conversion, and how the rendering intent handles out of gamut colors like maybe the blues in your sky. If the sky is clipping, then you can get issues too. 16 v 8 bit output may address some of these issues, but if the image is destined for the web, it is going to have to be reduced to 8bit JPEG at some point.
If you do not want to post a file, then the discussion is limited by speculation. If the sky is suffering because of your workflow, saving at a higher quality JPEG level of compression will not help - better to try to figure out which step of your workflow is the culprit and address that directly.
And there is "banding" in the above image, mostly in the red channel, but some in the green as well. Attached is a view of the red channel, with some contrast applied to make the problem more evident.
kirk

Image hosted by forum (
671891)
© kirkt [SHARE LINK] THIS IS A LOW QUALITY PREVIEW. Please log in to see the good quality stuff.