It depends on the circumstances and the person. You can take action immediately or a reasonable time later. Again, there are many factors.
If I saw my child doing something wrong, then immediate action may be warranted unless it is the "heat of the moment" and my emotions may drive me to act more harshly than is reasonable.
Adults are not children, in most cases. In Internal Affairs it could take weeks or months to deliver discipline. In many cases the matter should be discussed, as in violations of our agency policy and procedures. They are not typically matters that require a time sensitive response. I would present the facts of a case to the command staff and they would discuss the issue to ensure they were not only fair, but consistent in their decision with the person in question as they have been with others in the past.
In either case, wrong is wrong and there is no statute of limitations. Move too quickly at times and you may be accused of too speedy judgment.
The best advice I tried to give those under an IA investigation was this. If you did do something wrong and/or have made a mistake, the VERY best thing to do is to accept it, admit it and drive on. The people who accepted this advice faired very well in their disciplinary hearing. It was those who chose to argue and direct blame to others who did not.