Yes, it has to die. In this universe things can only grow indefinitely by less than an n^3 factor, because that's as fast as the lightcone of any event grows. Exponential growth, no matter how small the factor, will eventually outgrow n^3.

Once we attain the limits of what we can do in 2 dimensions, we aren't that many exponential growth events from what we can achieve in 3. Or once we achieve the limits of silicon technology, we aren't that many exponential growth events from the limits of photonics or quantum or any other possible computing substrate. Unless we somehow unlock the secret of how to use things smaller than atoms to compute, and can keep shrinking those, we're not getting very much farther on a smooth exponential curve.