Train your horses and log in next day will do it easily

do what you normally do and you will move up but you MUST login tomorrow. Very important MUST login tomorrow. Even if all you do is open the game and get credit for the obj. MUST login tomorrow. if you don't login 2 days in a row you don't get credit for moving up. I'm emphasizing the MUST login tomorrow because it doesn't look like you login every day so want to make sure that is clear. when someone asks this question I always check this. And I either emphasize the login tomorrow if they don't login all the time which you can tell if you drop in the ranks. or I point out how much they've gone up if they logged in yesterday just by doing normal stuff.

okay, thank you, I will try again. I did login yesterday and did my usual stuff and i still dropped. i did some extra stuff today so we will see what happens tomorrow. thank you!

Ranking is based on seniority, number of horses, the ages of those horses (up to 30), skills of the top 10,000 horses, and trophies won (with completed collections apparently counting for as much as a trophy in ranking points).

Just to give you a clearer idea of what to aim for specifically if just logging in isn't working. Training horses and breeding/buying more will also give you a jump.