Shyvana has been suffering from powercreep for so long
From memory, the last time I remember Shyvana having any relevence in a meta was back in season 3 or 4 when she could be played in the top lane. As time goes by with new champions being released people has started to lose favor for her when newer champions either offers more, outperforms her, or both. I personally think the 6.6 patch is what sealed her fate into irrelevancy. Or at least its where the burial began.
V6.6: March 23, 2016 _Twin Bite (Q): Second hit bonus damage reduced to 40 / 55 / 70 / 85 / 100% AD from 80 / 85 / 90 / 95 / 100% AD. _ That 40% nerf at Rank 1 Q is huge if it wasnt obvious enough. BUT WAIT, THERES MORE!
V6.23: November 22, 2017 Furry of the Dragonborn (Passive) OLD Shyvana gains 5 / 10 / 15 / 20 bonus armor and magic resistance, doubled to 20 / 30 / 40 during the effects of Dragon's Descent. NEW Shyvana gains 5 bonus armor and magic resistance, and each elemental Dragon her team slays grants her an additional 5 bonus armor and magic resistance.
So they took away her gaining armor and mr passively by leveling up. Now she has to earn them by having your team securing dragons. Making the passive to have the opportunity to have no value whatsoever. The most value you can obtain would be 30 bonus armor and mr, 5 initially and securing 5 dragons. However the chances to secure 5 dragons are extremely slim as not only there being a limited number but you're also at a time limit as well. For the last dragon to be killed around the 35min mark will now forever be replaced by Elder Dragons which does not increase her stacks.
They did buff her ult transformation though by making the dash uninterruptible which I thought it always need. So that was nice I guess.
So you might be thinking that this would be the end to her suffering. Buy you would be wrong!
V7.1 Burnout (W): REMOVED Dealing 20% increased damage to monsters
They did allow her E, Flame Breath, to scale off of 30% AD in 7.15 but nerfed her Q again to 20 / 35 / 50 / 65 / 80% AD from 40 / 55 / 70 / 85 / 100% AD. Is her Q now considered as one of the weakest if not, THE weakest skill in the game?
And then from 8.9 they removed her AP ratios from Burnout entirely and buffed her E to hell as overcompensation, from 30% to 70% AP. Quite practically shoving all removed damage to her skill shot when she was designed as a tanky on-hit reliant tank buster. Now she has no defensive stats to survive and now she no longer has any relevant damage to be a threat. Back then people usually reference champs getting constant nerfs Irelia'd but this is beyond that. Her balance design is incoherent as hell with ratios looking like it was developed from random and on top of being powercreep out of existence. There are now many champs that fulfills her role with similar mechanics but does it better in literally every regard but worse yet, the said champs offers more than what she can provide. She doesnt even fulfill any niche, you can arguably say she offers nothing. If you're having any doubts to what I said, the perfect champ to compare her to is Vi.
Also, that buff in the PBE increasing bonus damage to Dragons from 10% to 20% is a whole lot of nothing. Might as well give her 5 more MS while you're at it!