Without posting an error code, there can be a thousand reasons why the GTS isn't working for you... next time this happens can you please post a number?
Go to http://www.nintendo.com/consumer/systems/selectds.jsp
and on the left side you should see Error Code Lookup, and paste your error number into there. Nintendo will tell you how to fix the problem.
The special events are downloaded through Nintendo WFC, and to access it you 1) load up the game 2) go to the menu 3) DO NOT select your save, instead go down until the cursor is on Mystery Gift. From there, you "receive a gift" and choose "Nintendo WFC".