It's probably worth noting that these arrows appear to cause an implosion effect, and this seems to eat the drops on lesser enemies. I've not yet checked whether this happens from the shot making the killing blow or not; so far, I've only used them to soften heavier targets after finding out it ate all of my (red) Lynel drops on my first shot.
Thinking more about Customer Appreciation Day timings... While it hasn't been consistently at the same stable, it has always consistently been the first time I've talked to Beedle at whatever stable it's at that he gives it. The trigger could just be talking to him at enough different stables.
It feels like I interacted with him a lot more in my first game before I got it than in my later games, but I also took a lot longer to really explore to a lot of places, since I had no idea about the map past what the map screen said. This makes me feel like it's probably not based on how long one has been playing.
It doesn't rule out it being based on talking to him on a particular game day of the month, because I've never talked to him every day for long enough to rule that out, and it doesn't rule out the number of beetles traded because I didn't have that many to trade the first game. Tgape (talk) 20:21, January 25, 2020 (UTC)