... he loses a close game due to a couple errors made on easy grounders with bases loaded from 3 walked batters. as your packing up in the dugout, you hear him make a comment, something like "Maybe if you guys could field the damn ball we could have won this game."..
First, I totally agree with many GREAT points made by all so far.
One of the most important things to instill in a team is "team". Under NO circumstance should a P be allowed to call out teammate errors. Other important lessons are include mental strength and "control what you can control". He is failing at all of them. (I'm only talking about the conduct issue and not the performance issues)
I can relate to your situation being at a small school and how hard it is to sit a kid. I contend that it is worthwhile to take the short-term lumps (losses if necessary) in exchange for sending the right message and establishing the desired culture - sit the kid and communicate clearly what is right and wrong and what the expectations are if he wishes to enjoy the privilege of taking the field. I think you will find that, because the talent pool is small, it will have an even greater impact with the whole team. They will see clearly what is important to you and will ultimately rally around the struggling player to encourage him to straighten up in order to allow the team to perform at it's best.
Regarding the game scenario, it is also important to point out that those runs scored mostly because they reached base via his walks. And I don't see a problem with running or other types of extra work being part of the discipline/reward menu. It is not always feasible to send a immediate message with playing time and not all kids are motivated by the same things. You have to continue to identify what motivators work best for each individual and for each group as a whole.