The are a couple of things wrong with your code:

1. You have a return statement in every branch of your code. That means that you will return from the first iteration of the loop no matter what.
2. list.append modifies the target instance in place. As is conventional in Python for such methods, it returns None, which, combined with #1 means that you always get a return value of None.

There's also something very strange about your code. You flip the sign of a positive number by multiplying by -1. That makes sense. But then you take the absolute value of a negative number. Why? Flipping the sign is the same as multiplying by -1 for negative numbers too. And even for zero.

In fact, you don't even need to multiply by -1. There's already a "flip the sign" operator: unary -.

You can write your function as a single list comprehension:

def reverse_sign_of_nos_in_a_list(list1):
    return [-x for x in list1]

Without converting the number to a string:

def reverse_number(n):
    r = 0
    while n > 0:
        r *= 10
        r += n % 10
        n /= 10
    return r

print(reverse_number(123))

Let's Break Your Problem in 2 Function:

A function to reverse and a loop to read until you get a number or user cancels:

    def reverse_input(num):
        if num[0] == "-":
            temp = num[:0:-1]
            return (-int(temp))
        return int(num[::-1])
    
    while True:
        num = input("Enter Number")
        if num[0] == "-":
            flag = num[1:].strip().isdigit()
        else:
            flag = num[:].strip().isdigit()
        if flag:
            print("User input is Number")
            print(reverse_input(num))
            break
        else:
            print("User input is string")
            resp = input("Would You like to try Again? Enter Y to try and N to Cancel")
            if resp == 'n' or resp == 'N':
                print("Sorry Execute Again")

What does it do ?

• It reads input from user. Input returns string always.
• First, we check if Entered String had negation sign or not. If it is there we'll test string skipping negation sign. Otherwise, we will use whole string.
• We will check if entered string is number using built-in isdigit() function. And Call function to get reversed string.
• Function will reverse string and typecast to integer with sign.

Assuming that you want to preserve the sign, try this:

def reverse(x):
    ans = int(str(x)[::-1]) if x >= 0 else -int(str(-x)[::-1])
    return ans if -2**31 <= ans <= 2**31 - 1 else 0

It works as expected for all the edge cases introduced by the new requirements:

reverse(321)
=> 123
reverse(-321)
=> -123
reverse(120)
=> 21
reverse(-120)
=> -21
reverse(7463847412)
=> 2147483647
reverse(8463847412)
=> 0
reverse(-8463847412)
=> -2147483648
reverse(-9463847412)
=> 0