Obviously a concern for any developer, but what do you think is the point where the amount of games released from 3rd parties (or even first parties) is decreased significantly as a result of poor sales?

Is there ever a point where this occurs? 

Would you expect it to be different for different companies?

Of course I made this thread with the Vita in mind, so feel free to refer to that console in your answer, but it might be worth considering the Gamecube too- would you consider that a console that recieved less support due to sales, or for a different reason entirely?

Do lots of game releases lead to sales, or do sales lead to lots of game releases? If the answer is "both" - what if you have neither? How would a console get out of this catch-22 situation?

I do not understand a "catch-22 situation." I think other consoles have to die for others to be supported.

This is a good question, maybe it's just random during low points on the consoles life cycle..

Part of the reason why the PSP got so hot in Japan was that after the DS software market was saturated over there, the PSP base was ripe for the taking in terms of releasing content. There was not as much competition over there for certain companies to have to stand out. So, they went PSP and reaped the rewards.

The Gamecube...was simply losing by such an extremely wide margin that it had no base. None of the big games of the generation were on there except Smash Bros, an that was first party. If the GC had simultaneous Rockstar and Square Enix support, we could have had a whole different ballgame. But once again, that was an emotional issue. Nintendo does not play nice with others and they got reamed for it with a measly 21m consoles sold.