Sorry things aren't working correctly. A few things I'd like you to check/do:
* You're using the most current version of Draw, right? Version 3.3? If you're not, go ahead and update it.
* Also, Illustrator CC just had an update to version 2015.3.0 20.0.0. Can you make sure that the app is updated? Just check in the Creative Cloud Desktop App under the Apps tab. It will usually show there if you're not current. If it looks like everything is current, double-check by tapping the Gear icon in the upper right and pull down to Check App for Updates.
* After you check that Ai is current, log in with your Adobe ID to http://assets.adobe.com (My Assets - Mobile Creations - Draw) and make sure all your Draw projects are there.
* Then, sign out of Draw, restart your device, then sign back in to the app.
* After you do that, sign out of the Creative Cloud Desktop App (Click on the Gear icon, then Preferences, then Sign Out), restart your computer, then sign back in.
* After you've signed back in on the desktop, create a simple project in Draw and try the Send to Illustrator CC function again.
One other thing that you may not have noticed:
There's a new function in Illustrator CC (it's not in the rest of the desktop apps yet but will be):
Open Illustrator CC and on the splash screen you'll see a Mobile Creations tab. Just tap that and your mobile work should be there. (The attached image is what the desktop will look like.)
If you don't see the Mobile Creations tab make sure you're up-to-date on all your software Illustrator CC (v20.0.0) and the Creative Cloud Desktop App (v22.214.171.1242). If you have to update the apps, make sure to restart your computer afterward.
Let me know how things go.