Friskt "belongs" to the memory, not the trip. Minnet is neuter. Å ha noe i friskt minne or å ha noe friskt i minne are interchangeable, to have something in fresh memory / fresh in memory. (You remember it clearly since it was something that happened very recently)
Hmm, on hindsight, I could imagine that this is because with frisk, -isk is not just an ending. So with "logisk", there is "log", from "logikk", plus "-isk" as an added ending, while "frisk" does not consist of "fr" + an ending.
Tror du at det er forklaringen?