I ran into the same problem. Update sum with the following code in place of yours:

sum = int(sum//2)

Yes, that's TWO division signs. This returns a result rounded to the nearest whole number. You need that or else the new sum value will throw off certain iterations because of the remaining decimal value.

I never knew about the // operator until looking stuff up for this kata.

def add_binary(a,b):
#your code here
sum = a + b
answer = ""
while sum != 0:
part = str(sum%2)
answer += part
sum = int(sum/2)
return answer[::-1]

My code is able to solve all the fixed cases and half of the random cases. What is wrong with the code. Can anyone help Thanks