Okay so at first I was very hesitant to post this, but at this point I am convinced it has to be a bug. I have farmed Arcanist Doan in SM Library literally 25+ times with the same group of friends (we are a group of 4). And after all of those runs not a single Hypnotic Blade has dropped. So I am posting this here on the off chance that there is some strange loot bug in Classic. Note we have only been farming the dungeon with 4 people (not a full party of 5). So I have no idea if that is part of the bug.
Update
Went back with the same 4-man group (this time we were all about level 40) and it finally dropped after 2 runs. I guess we just got insanely unlucky, though I still wouldn’t be surprised if there was some weird loot bug.
I don’t think 25 instances is enough to make an idea of drop rates. You just got bad luck. That blade dropped the first time I killed that boss and it was also with a 4-man.
It’s dropped for me as well.
If you keep having streaks of bad luck, you could try farming for Hand of Righteousness between down-time. It has similar stats.
25 runs is more than enough when the drop rate is historically documented to be about 50% (shared with the staff). The likelihood of that happening is 0.000003%. Try flipping a coin 25 times and see if you can get heads every time. 
I have run this 6 times on my mage and every time the staff has dropped. Frustrating when there aren’t many options to pair with the off-hand from graveyard. This could happen 1.6% of the time, which is possible, but unlikely. Our party composition has been warrior, mage, paladin most of the time, with a priest thrown in on occasion.
I solo Library on my Warrior for cash and cloth, and I see this thing drop all the time- pretty close to 50-50, actually (I prefer the staff).
So if there is a bug, I do not think it’s in the drop rate. Instead, post your run composition and all of that jazz, in case something to do with that is what’s throwing off the drops.
Likewise, be sure to come back and post if/when you actually do see it drop, as the devs would likely need that info too.
Run composition: (Warrior, Mage, Rogue, Shaman). Regular group loot. We 4 maned the dungeon every single time with this composition over about a week. We pretty much stopped running the dungeon because we out-leveled it. Every single time the rod dropped. We were just laughing each time because it’s statistically nearly impossible for the dagger to not drop at this point. So we are convinced that maybe this is a bug when running with 4 party members with this composition?
Some more info:
Warrior was always party leader.
Warrior and rogue were highest level, shaman 1 level below, and mage 2 levels below. Ran it from low to mid-high 30s.
I would be very interested to see if others try 4-manning the dungeon with this comp and see if the same thing happens.
My group is very interested in this anomaly, so at some point we are going to run it again and see if there is any luck. We will also try getting a 5th to see if a full party of 5 affects the drop rate.
I just really hope this doesn’t mean there is some loot bug in classic that is going undetected.
Can confirm it drops for 5, as I ran a priest buddy through there with a full group and he got it.