Why do I finish on, say, 50% but the next day when I log on it is just 49%? It happens so often, even when I've done several strengthening exercises after achieving a certain percentage.
This might be because the exercises you did didn't cover all the topics you have learned, hence, the next day, Duolingo takes off a percentage for something not covered yesterday. If I were you, I would pay that much attention to the percentage fluency. When I learned "man, woman, girl, and boy" in French, it said I was 8% fluent. That is pretty hard to believe. Don't worry if it changes. It is most likely wrong anyway.
Fluency is based on (among other things) the strength of the words you know. Your words are constantly decaying, so you need to go back and strengthen the modules when they drop from gold. The decay rate is based on a variety of factors, including whether you used the clues when you last looked at the words.