I've re-downloaded my entire Sonar Studio X3e and Melodyne Essentials and reinstalled them, and same problem.  These problems make Melodyne and actually Sonar X3 useless to me...  I tried again on a brand new project, a single track, unmuted, and these are the results:
 
1)   When I Melodyne a clip, then save it, it works ok by itself. If I then try to paste it, it doesn't pass over the Melodyne changes to the pasted clip.  If I close the project and open it up again, the changes then show up on the newly pasted clip. 
 
2)  When I right click on a Melodyne'd clip and select Bounce to Clip(s),  the software does its thing, and the clip is rendered flat-line, without any audible audio on playback.  The audio is squashed down to a flat line. So I can't bounce the Melodyne changes and use them that way.  (Note that I can take a clip without Melodyne changes on it, and it Bounces just fine, no problem). 

What happens if you do what I suggested in Post #10? I am trying to get some diagnostics here...I've bounced Melodyne tracks literally hundreds of times, but I don't know enough about what is going on with your project. For example when you say you "save" the clip, do you mean save the project? And if so, is Melodyne still open or is it closed? Remember that Melodyne processing is not like a standard audio effect, it works on a region. There are many things you can't do while it's open (e.g., split a clip) because it's actively working on the clip, and therefore you can't modify the clip.
 
Also, show the Take Lanes for the track to see what's going on there. You mention it's a single track, but you don't say if it was just a single recording, or whether you recorded more than one pass or overdub in that track. The only time I can get Melodyne to flat line is under conditions involving a muted or soloed Take Lane.
 
This forum is filled with people who have been able to bounce Melodyne clips. But remember there have been many examples in this forum of a problem not being solved until someone mentions something they thought was not significant, but then turns out to be the source of the difficulty. If you have Dropbox or some other place where you can upload the file, do so and either PM the link or post it here. If you don't have Dropbox or whatever, then you can go to www.hightail.com and send the project to yourself. That will give you a download link that you can PM to me or post here, then I can download the project and see what's happening. What you are experiencing is not normal. You could also try contacting tech support.

Yes, this is driving me nuts. Obviously it's an industry standard, and how can I be the only one with this problem ? I gotta be missing an option or something somewhere...  thanks so much for your patience... being a newb, just discovered take lanes... looked at them, and nothing there is muted. 
Sorry, I initially responded about post #10, then overwrote it in an edit...  but that shift dragging didn't do anything different.
 
I've pared it down to the most simple situation possible:  copied a short audio drum loop clip into a single unmuted track on a brand new project.  Melodyne'd the clip, saved the project (tried Melodyne both opened and closed), copied and pasted the clip into the same track, next to the original. Saved the project again, closed it, opened it, and that is all I did. That is how I got to post #11.  
NOW...  check this out...  on this new project, now everything works as it should...  no bugs as described above... at first it didn't, because I didn't set up the INPUT (it defaulted to NONE on that track when I started the new test project). The Bounce resulted in a flat line audio.  (Exactly the same type of response as on the full project). Then, changing the INPUT to left channel of my Scarlett interface, it all worked as it should! No problems. So I got excited....
Then.... checking this option out on my full project, I had the Scarlett input selected, and the problem was still there. 
At least I was able to duplicate the problem, if not solve it. At the request of Melodyne support, about a week or so ago, I started a whole new project, copying over existing tracks, to see if it would resolve the problem. No dice. Will keep digging.  On this project I have so much data, it's huge, don't know if it can be uploaded, will have to investigate further.  
But there's gotta be some option I'm missing;  I've duplicated the problem with the input field selected to NONE. 
 
UPDATE:  Aaargh... don't know why I didn't think of it before...  I tried bouncing other vocal tracks on the same project, and no problem !   It actually works...  my gosh, what a dufus...    That one bass track has been giving me all this grief.  Nothing muted on take lanes, INPUT and OUTPUT selected properly, but no joy. Don't know why, but this certainly narrows things down...

As this seems to be only the bass track, is there anything "special" about that track? Is that audio data or MIDI into a soft synth?

Take Lanes... !     That's the problem...   No muting on the Take Lanes or anything else that I can find wrong, as in incorrect inputs or outputs...   just the fact that the take lanes are on that track, for some reason, just can't get Melodyne to work on that track.  Asked Melodyne support about it, and oddly enough, they don't seem to be familiar with Take Lanes.  
 
Perhaps somehow that track got corrupted...  needs further investigation.
 
So Anderton, you nailed it !   I still would've been scratching me 'ead about this without that tip !!!  Thanks much !  I will have to try another new project to further investigate, but at least I'm in business for now.