Can same medicine be resumed after gap?

Does resuming the same compound of a psychiatric medication work if there is a gap of, may be, 10 half-life of that medication? I have heard from a professional that after a long pause it has to be a new compound. When does resuming work and when doesn't? = ~ I used to be on Prozac 60-80mg for rumination problems. Then after some incidents I stopped taking it for more than 4 months. After 4-5months I visited another psychiatrist who prescribed me the same thing: fluoxotine/Prozac. As far as I knew, it wasn't supposed to work since there was such a long gap in between. Was I told wrong that if there is a long pause in those kind of medications then after the pause it has to be some other medication. The 1st professional who told me that, he also told me that pausing without notifying the prescriber is very frustrating for the psychiatrist. Please let me know if I was told correctly. Or if I wasn't told the complete story.