The word that describes maintaining your body on the water surface

Solution 1:

To flounder might be a suitable word.

From Google:

Flounder struggle or stagger clumsily in mud or water. "he was floundering about in the shallow offshore waters".

(To do it successfully would probably be treading water).

Solution 2:

You are looking for (to) float:

  • to stay on the surface of a liquid and not sink:
    • An empty bottle will float. You can float very easily in/on the Dead Sea because it's so salty.

(Cambridge Dictionary)