As noted in comments, there are many ways to reduce minutes to hours and minutes. However, to address your question as to why your approach is failing:

Object keys are treated as strings, not numbers. Also, you have declared time as a string.

For your approach to work, you have to make BOTH these changes:

let time="" -> let time = 0

and

time += key -> time += parseInt(key)

Working snippet:

console.log(TimeConvert(126));

function TimeConvert(num) { 
if(num<60 && num>10){ 
  return 0+":"+num
} 
if(num<10){ 
  return 0+":"+0+num
}

let object={ 
  12:720, 
  11:660,
  10:600,
  9:540,
  8:480,
  7:420,
  6:360,
  5:300,
  4:240,
  3:180,
  2:120,
  1:60
  } 


let time=0;


for (let key in object){ 
  while(num>=object[key]){ 
   time += parseInt(key) 
  num-= object[key]
  }
} 

 
  if (num<10) { num = "0"+num;} // add leading 0 and coerce to string if num <10;

return time+":"+num

}

Why not use this algorithm

1. Get the number of times that 60 minutes is in the number argument
2. Get the remainder minutes
3. Concatenate both (with padding for the minutes)
4. Return the answer

const getHoursAndMinsString = (num) => {
  if (num <= 0) {
    return `0:00`
  }
  const hours = Math.floor(num / 60)
  const mins = num % 60
  return `${hours}:${mins.toString().padStart(2, "0")}`
}

Your object lookup is just encoding n=>n*60, but only for a subset of possible values so is arbitrarily limiting the range of values your function can operate on.

Removing that, and using floor and % to compute the hours and minutes respectively reduces the code down to:

function TimeConvert(num) {
    let time = Math.floor(num / 60);
    num = num % 60;
    if (num < 10) { num = "0" + num; } // add leading 0 and coerce to string if num <10;
    return time + ":" + num;
}

These calculations can also be done inline if you rather which reduces the code even further:

function TimeConvert(num) {
    return Math.floor(num / 60) + ":" + ((num % 60) < 10 ? "0" : "") + (num % 60);
}

just watch out for negative values, or anything higher than 1440, which would overflow past 24 hours and you may want to start displaying with days.