Like players, your manager's stats can go up or down over time. There are various factors which can cause these fluctuations.
The main factor is how well your team performs compared to expectations. For instance, if your team is expected to finish 10th and ends up 5th, the manager will have done a good job and his ratings might increase at the end of the season.
Conversely, if your team was expected to finish 10th and ends up 15th, he will have under-performed and his ratings might go down at the end of the season.
Of course promotion and relegation can create the biggest change in your manager's stats. Getting promotion can boost your manager's profile (and therefore his stats) quite a lot, although the exact increase will vary from manager to manager. And as you'd expect, relegation can have a detrimental effect on his ratings.
A manager's ratings can fluctuate during the season as well. Winning awards (for instance "Manager of the Month") might increase his stats. But going on a bad run of form can have the opposite affect. Experience also helps a manager to improve – his ratings might sometimes go up when he reaches a career milestone, for instance 200 games in charge.
Finally, in the Pro version of the game there are a couple of ways that the chairman can help to boost his manager's ratings. You can appoint extra members of backroom staff, and these extra staff members will give your manager's abilities a boost.
And sometimes a manager will request to go on a training course over the summer – for instance a coaching course or a tactics course. These courses will boost his rating in the relevant area.