Is it stupid to give someone a second chance? Well for me, it's not. Giving him or her a second chance is doesn't mean you're allowing them to hurt you again, but instead you are giving them the opportunity to be better and change their ways.
Nobody is perfect. People make mistakes, what matter here is that they admit and regret the bad things they have done. If you can see that person is committing their selves that they sincerely regretted and dedicated to change , then why not . The effort is there just to win you back, give him that chance.
When you stop giving a person that second chance, you're denying him the chance to be a better version of his or her self. But let's say, you are already drained of " forgiving over and over and over again" scenario, it's a different story. You should know when to stop. You should always know how to protect your heart.