Outdated - CS50's Introduction to Programming with Python: Code does not break

I'm using the CS50's tutorials to teach myself python. I am trying to solve the 'Outdated' problem in problem set 3. The code works when I input date as 9/8/1636(i.e., correctly transforms date to yyyy-mm-dd and outputs the result) but not when I input September 8, 1636; it again prompts me for input. I cannot figure out where I went wrong.

The context to the problem can be found here, and the code i tried is copied below:

# Initiate the list
month_li = [
    "January",
    "February",
    "March",
    "April",
    "May",
    "June",
    "July",
    "August",
    "September",
    "October",
    "November",
    "December"
]

# Start infinite loop that breaks when a valid date is entered
while True:
    # Prompt the user for a date (format: 9/8/1636 or september 8, 1636)
    input_date = input("Date (in month/day/year order): ").strip()

    # Attempt to transform date into yyyy-mm-dd format
    try:
        # Split month, day and year by "/" separator and convert to integer
        month, day, year = map(int, input_date.split("/"))

        # Check whether month and day fall within expected ranges
        if 1 <= month <= 12 and 1 <= day <= 31:
            # If so, then print year, month, and date
            print(year,f"{month:02}",f"{day:02}", sep = "-")

            # Break out of the loop
            break

        else:
            # Check if date string starts not with a number but a letter
            if not input_date[0].isdigit():
                # Split the date by space
                month, day, year = input_date.split(" ")

                # A comma (,) will remain, so need to get rid of that
                day = day.replace(',', '')

                # Convert day and year to integers; will deal with month after
                day = int(day)
                year = int(year)

                # Capitalize month for case insensitivity
                month = month.capitalize()

                # Need to check if the month exists in the list
                if month in month_li and (1 <= day <= 31):
                    print(year,f"{month_li.index(month) + 1:02}", f"{day:02}", sep = "-")
                    break

    except:
        pass

Look at what happens. When you enter that string, the map(int... is going to throw an exception. That will skip to your except, which does nothing and loops around to ask for input again. You never get past the that statement.

What you SHOULD do is throw out the try/except, and move the if not input_date[0].isdigit() to the front. That way, you don't TRY to parse bad data.

while True:
    input_date = input("Date (in month/day/year order): ").strip()
    if not input_date[0].isdigit():
        # Split the date by space
        month, day, year = input_date.split(" ")
        ...
    else:
        # Split month, day and year by "/" separator and convert to integer
        month, day, year = map(int, input_date.split("/"))