You'll lose half of what you earned during the week, the other half carries over, and then a quarter of it will linger into the second week, then an eighth in the third week. It all stacks up as you earn merits each week. If you earned 750 all in one week, when the update happens you'll have 375 carrying over. Then you need to earn 375 more to maintain rank 3. The math gets fun after that, but basically you'd have to earn ~400 a week to guarantee you maintain rank 3.
EDIT: If you only care about holding rank 3, here's how the math works
Week 1 - you got 750 marks. Done.
Week 2 - 375 carry over, you have to earn 375 more.
Week 3 - 187.5 from wk 1 carry over, 187.5 from wk 2 carry over, you have to earn 375 more.
Week 4 - 93.75 from wk 1, 93.75 from wk 2, 187.5 from wk 3, you have to earn 375 more.
Week 5 - 0 from wk 1, it's gone. 46.875 from wk 2, 93.75 from wk 3, 187.5 from wk 4...NOW you must earn 421.875 merits to maintain rank 3
You can keep doing the math, but if you'll average 400-425, you're gold.