Possibly because it was now starting to get rarely used, possibly outclassed by other stallers that are immune to Quagsire's Toxic and can Toxic it back such as Toxapex and Amoonguss, which are both in OU. Its usage stats started to get lower too, as people find OU mons like Rillaboom and Amoonguss defeating it with their STAB grass type moves. Where did I know its usage stats dropped? Well, its here:
Once upon a time an OU Pokémon by usage, Quagsire has experienced an
extreme drop in usage throughout the last year. During the final
usage-based tier update of Generation VI, Quagsire dropped to PU.
Source if you want to read the complete article at Smogon.
Although there will be a suspect test for Quagsire in PU, I'm pretty sure it won't get back to OU. It gets wrecked easily, getting Taunted by Mandibuzz and Mew, as back in the good old days where no one knew how to counter Quagsire's Curse+Toxic+Recover stall, but nowadays, its easy to predict its a staller set.
A large number of the common stallbreakers that the PU tier has to
offer happen to be Pokémon that require boosting moves in order to
perform their role. Quagsire is the only PU viable Pokémon with access
to Unaware, an ability that allows it to reliably handle a number of
common boosting Pokémon such as Swords Dance Pawniard, Calm Mind
Duosion, and Substitute + Swords Dance Bouffalant. Quagsire's
introduction to the tier has severely constricted the pool of viable
stallbreaking options, making stall much more difficult to beat
because it limits the number of Pokémon that are able to do so.
Quagsire's ability to blanket check such a wide range of stallbreakers
works fantastically with other, more passive Pokémon such as Muk or
Bronzor, which can be fantastic supportive Pokémon on defensive
builds, but can otherwise suffer due to their innate passivity. This
further accentuates the matchup problems, as it means that there is a
seemingly larger number of games coming down to whether the stall team
can handle whichever stallbreakers are present in any given match
rather than how well they play.
This is the pro-ban argument from a Smogon article. But Quagsire dominates the PU tier, at least its what they're trying to say. So, putting it in PUBL or NU is what might happen if the pro-ban argument wins. If the usage stats get higher, Quagsire would probably place his comfortable butt on RU's chair.
Source at the same article as above.
Now, who won?
Quagsire's not gonna be in PU anymore, since 30 out of 49 voters voted BAN.
With over 30 of the 49 eligible voters voting ban, Quagsire's stay in
PU proved to be short lived, as it was swiftly banned.
Source is the also the same as above.
In my conclusion, it was just because there were many mons that make easy of Quagsire, as mentioned above. But soon, Quagsire won't be in PU anymore, as people said it was too broken to be in the PU tier. Or, what I mean by broken is too OP.
Here's a PU set most people use when playing with a Quagsire:
Quagsire @ Leftovers Ability: Unaware EVs: 248 HP / 252 Def / 8 Spe
There's an explanation for it and everything, but since I've come to my conclusion, these are the reasons why Quagsire went down to PU, but soon not anymore.
Hope this helps:)