Here's how I see this whole GC losing support thing.
Right now the console is losing support because 3rd parties simply overestimated either
a) the market penetration that they thought the GC would have or
b) how 3rd party friendly the console would end up being.
Probably a combination of both. GC sold under expectations so obviously the smaller then expected userbase is harming sales of 3rd party games, and, GC owners are mostly fans of 1st and 2nd party games. Bottom line, none of this is good news for 3rd parties.
That being said, there is still a market for 3rd party games on the GC, it might just be smaller then everyone thought it would be. So now the GC might lose the support of a few 3rd parties here and there (hopefully not too many) but the userbase will continue to grow and the remaining 3rd parties will have less competition, hence they will do better and eventually things should stabilize.
What Nintendo should do is make an effort to promote 3rd party games as much as they can like that commercial "180 games" or something. That certainly helped. They should also go online in a more significant way. Maybe then people would take them a little more seriously. I also think they should redesign the GC and give it a cooler and more hi tech look like they did for the GBA-SP.
If they're not careful this losing 3rd party support thing might spiral down out of control and they might end up with the kind of situation they had with the N64. Which doesn't mean the end for them. Nintendo are good at always turning up a profit not matter how bleak the situation is. It's just not a preferable way to go about doing things.