If you can save in Single player games then it isn't permissions - traderoutes are all saved in the same folder. With the same naming convention, containing tr - for trade route - the number of towns on the route - and what looks like an identifier for the type of route, with some random characters..... so four things to look at ...
1. are you up to date with patches - the version should be Version V 1.3.2-29411 BS - displayed on the opening splash screen. If not get the patches and update.
2. There maybe an issue with the traderoute folder - Create a Folder somewhere else (MY DOCUMENTS for example) and move the traderoutes individually - not SELECT ALL - but one at a time. Then delete the Folder. Create your new traderoute and save it - the game will create the ......\TRADEROUTE folder.
3. Create a subfolder in Traderoutes and 'move' your current save routes in to it. Then try to create a new one and save that. It just maybe that you are getting a duplicate name - unlikely but .....
4. The one you are going to hate - reinstall.
Uninstall - make sure you clean out the APPDATA for the game, save what you need games and trade routes somewhere in MY DOCUMENTS.
I would also - Run CHKDSK /F - see below - best to do this overnight on your disc it may take a while. Worth it now and again anyway.
Download the install files again or STEAM version use DELETE LOCAL CONTENT
Reinstall game on system disc C:
Chkdsk link from UK (otherwise seach MS.COM for 'chkdsk windows 7 command line')