Man, it really is lame that the "Mystery species" fish, in addition to being a huuuuuge pain to have even show up, then don't even seem to ever keep damage between play sessions despite being hard to catch. I've gotten lucky enough so far that I've gotten everything in my loop with just two left, but it's always nerve-wracking when I need it's my second chance at them (have 2 extra 3DS running just for this) since in addition to needing to do such insane things to have them spawn, you also need to get lucky with the random anglers you get, and then hope the game doesn't screw you and give you junk instead for one of your useful baits.
Maybe I need to figure out getting a better rod as it takes three "hits" on the Mystery species to catch it pretty much no matter what... but even then it's near impossible to get a three star rod to drop, and of course you can't combine the cheaper rods into higher levels...