There appears to be a bug in Basecamp that causes it to fall over when trying to import some of the information in these .GPX routes. See earlier post by Paul Webster :
http://www.walkhighlands.co.uk/Forum/viewtopic.php?f=20&t=44585&p=247681&hilit=easygps#p247681Two simple ways round the problem:
1) Use the (free) EasyGPS application to open the routes and transfer them to your GPS and / or save them. If like me you prefer to keep all your routes and tracks together in one place using Basecamp, you will find that the route files opened then saved from EasyGPS will be successfully imported by Basecamp.
2) Alternatively, instead of using EasyGPS you can open the original .GPX files with Windows Notepad and delete the lines of text starting with the one whose XML tag is "</extensions>" up to and including the one with XML tag "</extensions>". Then save the amended files and you will find that they can be imported by Basecamp.
Hope this helps.