I never had problems playing online before until a couple of months ago.  Around that time, my 360 started acting all wonky.  Even now, it will disconnect from time to time and tell me I need to adjust some settings.

The biggest annoyance has been playing 3DS online.  I've been getting disconnected a lot more, lately.  I use a router provided by my telephone company.  The only reason I even have internet through the phone company is so I can game online.  It'd be a lot cheaper if I just used DirecTV's internet or some other service.  The router has no logo or name whatsoever.  No idea who to call for tech support aside from the phone company.  No instructions.  No box.  The guy just set it up and left.  I don't even know how to protect it from random users that steal my Wi-Fi.

Anyway, the main issue here is the stability of the online experience.  Anyboy got some answers?  Keep in mind, you may have to dumb you answers down a bit.  This isn't my area of expertise.

Probably you're wireless router. When they start to go out and need to be replaced they will start dropping wireless signal.

...and you should use you're own routers that you can setup.

I have the same problems with online on 3DS. I don't think I have EVER successfully connected and finished an online Mario Kart 7 race.

Anyways, I've checked around online and I found this. Haven't tried it but I hope it helps.

http://www.ign.com/boards/threads/error-006-0612-for-mario-kart-7-here-is-the-fix.207270456/

just reset( unplug replug)

Superchunk and pezus are correct, you need a new router. I had the same issue a few months back, and that fixed it instantly.

There are plenty of cheap but good ones out there, and installing them is really, really easy. Even this cheap piece of junk (http://www.amazon.com/Netgear-WGR614-Wireless-G-Router/dp/B00008SCFL) has been working well for the past four months.

When you buy the router, just follow the simple included instructions for installing it, and you'll be good to go. The instructions should also include directions on how to secure your connection, so random folks can't go about stealing it.

Then it's settled. Tomorrow, I go to the mall and buy a new router.

I have one sitting in my closet not doing anything.  You want it?

That'd be awesome!  I'll be right over!!

As soon as I read this thread I knew there would be some smart ass answer like this