The Sims 3 Launcher keeps asking me to log in

@aodoherty  Does the same thing happen in a clean Sims 3 folder?  Actually, before you go that route, delete the file with your email address in the name in Documents\Electronic Arts\The Sims 3\Downloads, and see whether that helps.  If it doesn't, try the clean user folder.

Please also clear both the cache for Internet Explorer and the one for whichever browser you're using to download store content.  The launcher uses IE, and your browser will be involved too.

If these steps don't help, try changing your password to something with only letters and numbers, no special characters, accents, or really anything you wouldn't find in English.  The launcher periodically stops working properly with certain symbols, for no apparent reason, and that can also sometimes cause exactly this problem.  No idea why.

I have this exact same issue, even stranger is that it was working fine and I was about half-way through downloading and installing my paid content and then this issue started.  I'm only have about half of my paid content installed and I'm not able to finish the rest. 

@cowsnap  Please move the entire Sims 3 folder out of Documents > Electronic Arts and onto your desktop, open the launcher to spawn a clean folder, and try to download one Store item, something that worked without your needing to input your password before.  I'd like to know whether a switch flipped, so to speak, and now the launcher is forcing you to login for everything; or the issue is something you downloaded.  In the latter case, please let me know which item(s) you were trying to download when you first ran into the issue.