When should you avoid a third bean field in Bohnanza?
I would never, ever buy the third bean field in Bohnanza except as a last resort (and yes, I win at least my fair share of games and consider myself a good player).  Look at the final scoring margins of your games: is the winner usually ahead by half a dozen points or more?  In my experience, this is not the case, it's usually much closer than that, and as such, those 3 coins you spent on a third bean field could be the difference between first place and a much less auspicious final position.

Of course, the question really is, does a third field usually pay for itself, or not?  Obviously it can pay for itself.  But shrewd bargaining, good timing, and paying attention to what cards have been cashed in for gold do too, and I think working hard at improving those skills is way more important than getting a third field at the earliest opportunity.  The third field makes the game feel a lot easier - once you have one, you will very rarely be at risk of losing a crop before you have a chance to make some gold out of it.  In my experience that leads to complacency and complacency leads to less profitable bean farming!  

In short, either you regularly find yourself with not enough fields to make money with, or you don't.  If you don't, you don't need a third bean field.  If you do, I feel like you could probably benefit from tightening up your game a little - the bean field is an easy but expensive way out of your problems.  In one of Uwe Rosenberg's other fine games, At The Gates of Loyang, there's the option to increase the size of your storage barn for a small cost, at which point you can keep 4 vegetables from one turn to the next instead of 1.  And I feel that it's a trap in that game too: if you are regularly producing more vegetables than you can use, you're doing something wrong.  Unless you've exhausted all the other possibilities for fixing your supply/demand imbalance, you want to be VERY wary of spending your valuable coins!