Hi Catherine,
Welcome to the forum! I believe you are asking about cold
processed soap; not cold-pressed soap.
When you re-melt cold-processed soap, that is called "rebatching."
Rebatched CP soap is entirely different than melt-and-pour soap. M&P is a pre-processed soap base specifically created to be meltable. It will produce a very smooth bar, whereas rebatched CP usually looks somewhat rustic, more like HP soap.
Now that we have the terminology straight, please know that CP soap can maintain its fragrance just fine. If you are reading from a source that makes a blanket statement saying otherwise, I'd question that source as being one upon which you want to rely. Yes,
some scents, such as citrus EOs, do tend to fade more quickly. But most FOs designed for CP soap are quite stable and long-lasting, and many EOs last just fine, too. That being said, I do find that I need far less fragrance in my M&P bars than I do in my CP bars.
I recommend reading some of the threads here about different FOs and EOs to get a sense of which ones tend to "stick" the best. You can also learn the basics of CP, HP, and M&P, and then decide which one will be best for what you want to achieve.
Happy soaping!