The two themes to success on the above mentioned species are cool water and obtaining small individuals collected properly it seems. Not only are smaller individuals more apt to feed, but they decompress better from what I've seen.
The only documented peppermint still alive today (this was after speaking recently with four Japanese guys that know the market well... two major shop owners, and author, and a diehard aquarist) is an individual in Japan that was collected at about the size of a quarter. It's been alive for about seven years and is kept in a dedicated setup with water chilled to 22 Celcius (72 F). I think it's been about three years since Chip Boyle collected this species. The shallowest documented boylei I think was around 150 feet. I've kept a P. multifasciata for years now that I got small. Long term success with Centropyge hotumatua shows that these guys too must be kept cool.
As for the personatus, two of the four the Waikiki Aquarium has that are still alive were collected at Midway in '92 when small in 80 feet of water... wouldn't it be nice...

A captively kept pair of personatus collected as adults did settle in for the long term, but it was a bear getting them to feed even in cool water. With the guys out in Hawaii getting trimix certified on their rebreathers hopefully they'll fish some out soon! They've already just got some more Bodianus sanguineus. Tourism to Midway is supposedly opening back up soon for those of us that dive mere conventional scuba... even B. sanguineus are found shallow there...
Centropyge abei is in the same boat and the one individual in captivity is now on display at Waikiki and looking much better than when Charles got it! Bright colors and a full body... what did it take to get it feeding? Dropping the temperature was it and good old TLC... Through the chain of collection it was kept in very warm water. I think it's at around 72 now after being in the high 60s for a while during recovery... maybe Charles could share a photo

A C. abei juvenile was seen earlier this year over a period of about two months in southern Japan at a depth of just 15 feet! There's a photo in the new "Aneglfishes of the World" book that will be out soon... amazing... but it was in shallow water that was 63 degrees!
I think their cool water requirements will always limit how much these species are kept, even when they become available aquacultured. I chill a few of my tanks down to 76 for C. resplendens and others, but going into the low 70s starts effecting more tropical species and results in one heck of an electric bill! I'd imagine that even when kept at the higher end of their temperature range that their metabolism would be higher and their lifespan shorter in the long term... If anything did warrant a chilled species specific tank it would be a peppermint or personatus though for sure... 8)