Hello DC. I honestly couldn't figure out what problem you were describing, but after looking at your photo your issue became apparent. To at least start with a clear description of the problem, the little islands of wood that you want to remain within the loops of the script letters "e" and "l" are falling away/flaking off, taking their bits of attached surface paint/stain with them. That results in the visual defect you are encountering, and that is what you would like to prevent in the future.
The problem is not your bit, it is not the wood, it is not the stain. It is a combination of factors. Some types of wood and other materials may cut fine with your bit, and not have those little inner bits of the letter loops fall off. Other types of wood and materials could have been much worse. If for example, say you are cutting this text in MDF, some brands of MDF may hold these little details better than other brands............ And maybe with some other bit, but of the same carving angle, things may have turned out well. Maybe with the bit you used, but a different feed rate or RPM, or combination there of, things may have turned out OK.
This is where you have to learn what bits work with what materials, what feeds and speeds work, etc. This is mostly from your own experimentation. I used to have a stack of boards of different materials with test cutting designs on them, and some cut with different bits. Learning what works best come down to you experimenting and keeping track of what you discover works for you and your machine.
As a note, clear descriptions, and clear photos will be needed for you to try and get clear answers. Good luck and welcome to the forum, Chuck
Chuck Keysor (circa 1956)
PRT Alpha 60" x 144" (circa 2004)
Columbo 5HP spindle
Aspire 9.0, Rhino 5