These are all the things I could think of, so please tell me if I should add something to the list.
If Shuckle runs out of PP, it struggles and (almost always) damages itself faster than it can heal. This also means Shuckle can't use cosmic power, so the opponent can reset your stats and they'll stay reset forever.
If an opponent has so little HP that it can damage Shuckle faster than it can heal, the Shuckle faints. (this is especially easy for Pokemon with unaware, night shade, or seismic toss)
Dark Pokemon are immune to status moves that are prioritized by prankster, so they won't be affected by soak, leech seed, and taunt.
If Shuckle's item gets nullified or removed before it activates, Shuckle can be poisoned.
If the opponent has prankster, it can use taunt or curse before Shuckle can use taunt.
If the opponent has magic bounce or magic coat, it will bounce leech seeds and taunts to Shuckle. Thus, it'll be able to taunt or curse Shuckle. If your opponent predicts a taunt and switches in a magic bouncer, the Shuckle's dead.
If the opponent has magic guard, it won't let leech seed heal Shuckle, so it faints eventually from burn damage.
If the opponent uses core enforcer, Shuckle will lose its ability and become vulnerable to taunt and curse.
If the opponent has oblivious, it's immune to taunt.
If the opponent has a mental herb, then Shuckle will need to use taunt twice to taunt it, and the opponent gets one chance to use taunt or curse.
Conclusion: Nothing is invincible.
I was too lazy to list all the sources here, but if you want a source for any part of the list, I can link to a Bulbapedia article.