Store bought content keeps uninstalling.

I had this same problem and the reason was corrupted ccmerged-file. I deleted everything from DCBackup-folder (made copy of ccmerged-file first and placed it to my desktop for backup if something goes wrong), and then downloaded Nona's Sims ccmerged-file from here:

 https://nonasims.wordpress.com/2012/05/17/dcbackup-ccmerged-package-and-your-premium-content-items/

The correct file can be found in the last Q section of the main article ("Q: but I install my store content as package files or I really don't want to create a ccmerged.package.")

Place the downloaded ccmerged-file to your DCBackup-folder (make sure there is nothing else in the folder), and after that it should work perfectly. 

Let me know, if this resolved the problem.

Edit: Remember to turn off the EA App's Notifications (from settings) so that Store content shows up correctly in your game.

JonnyLooney​  If you've been reinstalling your Store content without removing the files that held the previous content, that's probably the current issue at least.  When Store content disappears from the launcher, it doesn't typically disappear from the user folder; it's just that the files are corrupted and the game can't read them.  So installing on top of that leads to more corrupted or unusuable files.

Point is, you'll need to rebuild your Store content in a new folder, then transfer your saves and anything else you'd like to keep to that folder.  Please see the two replies to this thread (how to install and installing into a clean folder) for more details:

[Read First] Sims 3 Store guide | EA Forums - 11157679

If your content disappears again in the future, make sure the .ebc files are still present in DCCache.  If they are, try deleting the SigsCache folder, in the same Sims 3 folder, rather than reinstalling the content.