Haskell: Procedurally generating level without slowing down

To better learn Haskell, I'm trying to basically build a variant of the well-known Indie Game Super Hexagon.

I am however having a problem with the level generation:

Right now, level generation is done by having a list containing all different "gauntlets" (patterns of walls, implemented as [[Bool]],a variable number of rows, each containing True or False for ); these are the building blocks of the level. Using the getStdGen() number generator, I'm able to create an infinite list of gauntlets.

However, at a single time, we only want to render part of these. To keep track of if a gauntlet has already been passed or not, a second argument is introduced, containing the sum of the number of rows of all gauntlets before this one. (e.g, length (gauntletData currentRandomNumber) + snd $ randomGauntletList !! (n-1), where randomGauntletList has the type [(Gauntlet,Integer)]

The problem is in how this list is used in the rendering function and the updating function: take 30 $ dropWhile (\(_,distance) -> currentDistance > distance) randomGauntletList

The dropWhile results in the program taking longer and longer to return the current 'starting point' of the list, therefore slowing down the game after +- 30 seconds.

I'm out of my depth: Is there a way to solve this problem?