had this happen to a friend of mine, just thought I'd toss this out there since I've never actually read this stated anywhere
You can only have one Trials weapon quest open (I'm assuming it has something to do with the Annals of Truth key item or whatever it is) before an NPC will allow you to open a new one
let me explain
friend of mine had been helping his gf's char for CoP and so erased nin af memory in order to request the katanas (as he had tossed them in favor of yotos or w/e). his nin was about 65ish when requested them, thought nothing of it, CoP is going well bla bla
Kodachi of Trials time, 254 skill, oh hey Ryoma, me again bla bla -- "Get out of my face."
so my friend (it's honestly not me lol, i felt real bad for him by the end of the day) tried zoning, no dice, tried a couple other things, no luck; so he figured it had something to do with erasing his AF memory
i told him ffxiclopedia (sorry wafik; showed no pre-req for the wsnm quest and couldnt think of how else to help him, so he tossed his AF and requested all of it lol, killed the brd sahagin etc, the lame night only with selbina cs and like 6 hours later we mentioned it in passing and someone on LS is like, um ya it's liek Borghertz Hands quests, gotta finish one at a time
he totally forgot he never went to kill Detonator NM.......
harsh
ps - i seem to recall a LS friend having more than one trials weapon, but i think once you've traded it back to npc and get key item, you can't get a new quest opened