Problem

I started my game and got a missing objects warning
My launcher shows all my stuff as uninstalled

Cause

It seems that certain updates (Origin or the game) can break your installed content and make it uninstalled.

In case of the launcher showing them as uninstalled, that might just be the launcher. Check your game if you have the stuff or not.

Solutions

To solve this, you probably need to reinstall all your custom content (including Store). Unfortunately this does not seem to work for everyone but I don’t have a solution if this doesn’t work.

If you get a missing object warning you should immediately leave your game without saving. If you save, all your houses and Sims will look different cause the downloads you used will be replaced.
Go to this folder: [User Directory]\theSims3\DCCache and find a file called missingdeps.idx. Delete this file. It’s a cache file that will be recreated on the next start of the Launcher.
Open your Launcher/game to see if you have your stuff back. If so, you’re done here. Else continue with 4
Close your Launcher.
Go to this folder: [User Directory]\theSims3\DCCache and move all files *.ebc (store) and *.dbc (3rd party content) files to your desktop (make a folder there).
If you don’t have your 3rd party downloads backed up, only delete the ebc files but it might not work as well if you do.
If you have any Store Worlds installed, go to [User Directory]\theSims3\InstalledWorlds and delete the files.
Open your Launcher. All your stuff will be uninstalled now (except houses/sims)
If you don’t clean out your downloads folder, you can simply reinstall everything but I don’t recommend to install everything in one go. If the *.ebc/*.dbc files are getting too big, the launcher has new problems. Keep them to 200-500 MB in size, depending on your computer. If you usually move the files to a save place, copy them back into the [User Directory]\theSims3\Downloads and then install.
If you don’t have those files anymore, you will need to redownload them. Store Stuff can be downloaded from your purchase history.
Close the launcher
Open the launcher/game and check if everything is back. If not, I don’t have any other solutions atm
If everything is back to normal, you can delete the files you have moved to the desktop in step 5

Precautions

To easily get your stuff back when an update decides to uninstall everything, you should backup the files in DCCache and Downloads every time you successfully install new downloads. Keep 2-3 backups in case one breaks.

Backing up the Store-Downloads is a good idea anyway in case EA decided not to host the files any longer. After you downloaded them to your game, you can find them in die Downloads folder.