I think that there is a lot of human nature that comes through in sports. A team that gets down in a series should get more desperate and focused, while a team that goes up may let up some. Just like in real life - once someone achieves some level of comfort its hard to maintain the hunger that got him there.
This is mostly in line with what I was thinking. While, idealistically, "every baseball game is a fresh start, a blank sheet of paper", in reality, that is just not the way it plays out. I think the better team typically shows up and plays good focused baseball, wins game 1 and then tends to mentally relax a bit too much with that same opponent in game 2 and 3. In their minds, the subsequent wins are almost a foregone conclusion and they tend to "mail it in". Once that competitive edge is softened, it becomes hard to just flip the switch back on until the environment changes (next opponent/next series/jolt of the loss to lesser opponent, etc.). I think there are a number of factors but I think this is a biggie.
As Somebaseballdad points out, baseball is quite difficult to play successfully - even more so when you are not fully focused and engaged.
BLD mentions the strategy of adjusting the pitching matchups, i.e. - saving your #1 for their #2 or #3 in efforts to take one game of the series. I thought of this and, undoubtedly, it happens from time to time. I have not dug deep enough to really know to what extent. But, I think this is relatively an exception scenario as compared to what I describe above. I do know some college coaches who's egos are just too big to allow themselves to take that strategy. And, besides, it sort of sends the wrong message to your team, even if true (our only chance is to win one game by sending our best starter against their worst starter). Also, there is usually a set rotation that tends to remain consistent for proper rest purposes.