The improvement of players happens at different times during a season, known as bumps. When these changes happen depends on the player and how much depends on the coaches, playing time, training budget (maybe) and the players themselves. There are generally 5 playing bumps during the season, that does not include the bump from Spring Training. So that equates to about every 30 or so games, but also depends on playing time and the player. From watchful examination, those with a higher Overall rating and playing time get bumps first in the sequence. If a player saw considerable playing time in Spring Training and did not see a bump, he will normally receive a bigger bump when the first one happens, so don't despair.
For those that are wondering, a promotion bump doesn't mean an extra bump during the season either, it appears that is a compilation effect. Could a player see a bigger increase in a promotion bump if executed at the right time is actually unknown. At the end of the season a player could get a promotion bump if he hasn't had his 5th bump, but that doesn't mean he will either. Players that don't get a 5th playing time bump will probably see the increase during rollover or promotion during Spring Training next season. A player could get the 5th bump if playing during the playoffs also.
Not all ratings are bumped during the season and only occurs at rollover and is affected by the training budget, playing time and the player(maybe medical also). These include: Arm Strength, Durability, Health, Speed, Patience, Temper, Makeup, Power, Stamina, and Velocity.
If a player doesn't receive a playing time bump he could in fact be stalled, meaning he is above the playing status of available coaching at the level and needs a promotion. This is rarely seen actually with players that have 3 or less years of pro experience. However other factors could be involved, such as playing time and players playing injured that you don't know about.
Do players get frustrated because they know they are not good enough for a ML career? Do they play for the love of the game? Do they feel unloved due to the lack of promotion? Do some feel they are better than they actually are? These questions and others probably go through a players mind in real life also.
Why do players slow down in their 4th year has mystified me somewhat. I can understand the first three could be classified as formative years to pro life. Does the pressure build once AA and AAA is attained? Is it because they should be close to their projections with little to improve on? Does monotony set in? Why do they slow down so much once they reach the majors? Don't they want to be the best? My answer to this seems to lie in the players physical abilities. They tend to be almost maxed out at this point, once that happens they tend to slow down in the other areas. The only way to battle this is with coaching and playing time.
Observations: Good young players will generally see a 4 to 7 point overall boost at rollover. 4th year players and above will see 1 to 4 point overall boost most generally at rollover. Young players with a low patience will see the highest boost at rollover especially in their formative years and could see an increase up to 10. Is that because they are more motivated to get promoted?