How quickly do I need to write up an employee for a performance issue?

We recommended addressing the performance issue with the employee as soon as possible.
First, feedback is more effective the more quickly it’s delivered. Waiting to provide feedback increases the likelihood that the employee won’t remember what they did wrong and that they may make the same mistake again.
Second, waiting to provide feedback risks sending the wrong message. The employee might feel that their mistake wasn’t that big of a deal since you waited so long to address it. Worse, they might associate their being disciplined with something else they did more recently—like bringing up a safety concern, reporting harassment, or using sick leave or FMLA.
That said, there are legitimate reasons to wait before disciplining an employee. If the employee went on leave immediately following their performance mistake, for example, you would usually want to wait until they returned to work before addressing the issue. You might also need to wait on any disciplinary action if the incident requires an investigation to determine what actually happened.