Javascript: Multiplicative Persistence Problem Proposed Solution Execution Timing Out

I have the following problem:

Write a function, persistence, that takes in a positive parameter num and returns its multiplicative persistence, which is the number of times you must multiply the digits in num until you reach a single digit.

function persistence(num) {

  let count = 0; 
  let numStr = num.toString(); 

   if (numStr.length === 1){
     return 0
   } 

   if (numStr.length === 2){
     while (numStr.length > 1){
       count += 1
       numStr = (Number(numStr[0])*Number(numStr[1])).toString() 
     }
   }

   if (numStr.length === 3){
     while (numStr.length > 1){
       count += 1
       numStr = (Number(numStr[0])*Number(numStr[1])*Number(numStr[2])).toString() 
     }
   }

   return count 
}

persistence(999) //solution 4

I'm getting "Execution Timed Out (12000 ms)" error. I know there's different ways to tackle this problem but I want to know specifically what is wrong with my code.