I think there are several reasons we haven't seen a major leaguer hit .400 since 1941. Part of it is because of the rise of
relief pitching, although I would argue that it has less to do with stamina and more to do with
familiarity,
scouting, and
platoon differential.
If you face a pitcher three or four times a game, multiple times throughout the season, you will see his entire repetoire of pitches. Whether he's throwing smoke or not, you're better equipped to deal with whatever he throws. That doesn't happen anymore. There are more teams in each league, so hitters faces each pitcher fewer times. Starters pitch every fifth day, instead of every fourth, so hitters faces each pitcher fewer times. And starters don't pitch as deep into ballgames, so hitter face each pitcher fewer times. Add all of that up, and as a batter you're less and less familiar with pitching as time goes by.
Some other reasons there hasn't been a .400 hitter.
The increased importance of the home run. Fans want home runs... they love home runs. It's great if you can hit 200 singles in a season and play rock-solid defense. If you don't hit home runs, people don't come out to see you. Swinging for the fences results in a lot of fly ball outs. And since you're swinging for the fences, you're not sacrifice bunting, which is a great way to NOT hurt your average.
The decreased importance of average. It has become less and less important to hit for average. Statistics like on-base percentage and slugging percentage are considered a better benchmark of hitting prowess.
More night games. With the exception of the Cubs, there are almost no day games outside of the weekends. It's much easier to hit during the day than at night. Todd Helton batted 29 points higher during the day than at night. Nomar Garciaparra hit 18 points higher.
Increased travel time. Prior to 1950, the furthest south AND west a team would travel was St. Louis. Three teams in New York, two in Boston, two in Philly, two in Chicago. Not a lot of travel time. No late flights. No West Coast road trips.
The media hounds. Any player hitting .400 or better in June can expect daily interview requests from reporters. June! Unless you're really good at dealing with the media (read: Mark McGwire), the pressure of a constant media circus is too much to handle.
There are certainly some other reasons why no one has hit .400, but maybe the best reason is this: It's fucking tough. Hitting a baseball is the hardest thing in sports to do. And if you only fail 70% of the time, you're considered one of the greats.