I think when it's something teachable, you would definitely want to exhaust all options before letting them go. I feel like with all the problems that can come from the hiring and firing and chances you are taking with a new person to have the same problems and more.
At the same time, my biggest point, is be on time. To be early is on time, on time is late, and late is unacceptable. I understand things can happen from time to time, but if it's always happening, then there is a bigger issue needing addressed and problem some work on their morning routine. But you can only help so much, everyone has to pull their own weight and be willing to put in effort. So if you have someone willing to learn and grow keep them and work with them. But if they are not taking accountability for their actions and trying to improve, then I would say it's time to move on.
