Typical rule of thumb is 7 years for this stuff. If you look at your credit report, you will see payments date back to at least that long. Creditors are compliant when it comes to removing mistakes or old debts that were either paid off or exceed the statutes of limitations (I have first-hand experience here). They are NOT however very lenient when it comes to fudging the numbers when it comes to your payment history. This is one of the most important factors when a bank issues you a line of credit (or insurance, phone, utilities to determine if you are risky enough to need a deposit when opening an account, and what your rates will be). If you don't make your payments on time, regardless of the situation, creditors need to know that information to determine the risk of lending to you.
Usually if you know you are going to be late making payments, depending on your circumstances you can work something out with the creditor to avoid having this negatively affect your score, but that can be tricky too and it's all at the discretion of the creditor. It's better to try to work this out before the bill is due rather than wait to communicate until after. That's on you.