I'd ask the frog "If yesterday I had asked you behind which door are the Riches and Power, what would you have said?" and then go through the opposite door.
Plot twist: The frog says: "I would have said: I have no idea what you are talking about". Explanation: the puzzle was created today. The every second day rule only applies starting from the day the puzzle is created.
Actually, asking "if tomorrow I ask you" is equally unsafe, since it could be that this is the final day before the puzzle is dismantled. To be safe you need to go with something more creative like "true or not, if we pretend this puzzle is still active tomorrow, and I were to ask you
But perhaps a more elegant solution is just "if the days you are lying and telling the truth had been reversed, and I asked you