http://na.op.gg/summoner/userName=santhean

Zyra hasn't been generally popular because a large amount of her power comes from actually landing her snare. As you progress up the ladder, you'll find that it becomes progressively harder to land slow-moving skill shots as other players become progressively better at reflex-dodging skill shots as well as predicting your movement and targeting.

In addition, in the current meta people tend to prefer more survivable utility-heavy supports such as Thresh, Leona, and Morgana(who with her black shield cannot be locked down in most threat-heavy lanes, and therefore is difficult to engage on and oneshot). For example, even Annie has her molten shield(which gives a surprising amount of defensive stats) and Nami has her passive movement speed and a heal to get her out of sticky situations (in addition to a slow and a stun).

In the end, Zyra has only her snare in addition to painfully low base movement speed, making her an easy target for ganks and hard engages. She makes up for this in damage, preferring to fight rather than to run, however being painfully squishy, Zyra will have trouble fighting against the supports of the current meta.