[yorwba]

  while grid[index] == 9 || grid[index] != 0 {

is equivalent to

  while grid[index] != 0 {

so when you backtrack, you always backtrack all the way to the beginning.

I think you want

  while grid[index] == 9 || initial_grid[index] != 0 {
    grid[index] = initial_grid[index];

or something to that effect.