According to the principle found in paragraph 127 both permanent and prominent should be written pr – mn – t. But prominent is written pr-o-mn-t. I am assuming this is just one of those things that you encounter in learning anni but wondered if there might be some reason that i missed.
For the first one, the "o" is inserted to make it legible and distinct in transcription. There is a good drill on similar words in the second edition of Gregg Speed Studies.
"Retrial" is written with the re- because it is a derivative of "trial." Same thing happens with "retrace."