In real life Ty Cobb, for the time span from 1910 on, played in 150 or more games in only 3 seasons (out of 19) and in 140-149 games in 5 seasons. That's less than half (8 of 19). Except for two seasons (1922 & 1927), he played in less than 130 games, with a high of 128 and a low of 79, for the other 11 seasons. I'm guessing that he's not going to be healthy enough to play a full season for the rest of his career in your case.
You could try setting the injury level at low to see if he could stay healthy longer but I don't know if it's going to help him in this case.
Also, he only had 600+ at bats in 2 of his 24 years, 1907 (605) and 1924 (625).
http://www.baseball-reference.com/pl...cobbty01.shtml