How many times will we go through the deck before the island is sunk?
In Forbidden Island the treasure deck has the following breakdown:

5 each of the 4 treasures
3 Waters Rise!
3 Helicopter Lifts
2 Sandbags


Depending on the difficulty the Water Meter will begin between the 1st and 4th tick, giving you between 8 and 6 remaining ticks respectively.
This means in a game that you can cycle through the treasure deck between 2 and 3 times.

You can find a breakdown of the game contents in the rules