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There are many tragic aspects of Zeus and Hera's relationship, but this is perhaps one of the worst: Hera is bad at her job.
After countless millennia of coping (through various methods) with Zeus's wandering ways, she eventually reaches a point where she can cope no longer. All of the love that she once had for Zeus is gone. The sparks are dead. Her patience has run its course. She's lost any hope that he will ever change for the better.
At this point, most women would leave. Actually, scratch that -- by this point, most women would already have left. Unfortunately, for Hera that is not an option. Even if she could bring herself to turn her back on the sanctity of marriage, it's extremely doubtful that Zeus would allow her to divorce him, and -- as both the King of the Gods and her husband in the mythology of a very strictly patriarchal society -- he holds all of the cards. Even if she skipped the divorce and just tried to flee, there's no place she could go where Zeus or one of his agents wouldn't be able to find her. She's stuck.
So Hera is the Goddess of Marriage, but she's trapped in a loveless relationship with the biggest womanizer in the universe. Her own marriage is a flaming train wreck -- arguably the most infamously dysfunctional one in the history of literature -- and since it's the only one she's ever had, that means that she has effectively zero successful experience in the area that she's trying to oversee.
She could also be seen as the Goddess of Motherhood. Unfortunately, that hasn't really worked out for her either, because she's a horrible abusive mom who threw Hephaestus off of the top of Mount Olympus as a baby because he was ugly. Both of her sons are disappointments -- Hephaestus because he's ugly, and Ares because he's a cowardly and chronically-humiliated warmonger who is constantly bested at his only job by Zeus's daughter from a previous marriage (who also happens to be his favorite child). Most of her own daughters seem to be well-behaved proper ladies, but that's just about the only thing they have going for them; they're all so overlooked and unimportant that the most famous thing any of them ever did was marry one of Zeus's bastards (Hebe and Heracles). An expert on lovingly raising successful and well-adjusted children, she is decidedly not.
Then there's her role as the Goddess of Rulership. Except that that's an even emptier title than the other two, because functionally, she's nothing more than a trophy wife. She became Queen of the Gods because Zeus willed it so, and she retains the position for the same reason; he's made it clear on multiple occasions that he could have her removed pretty easily if she tried to oppose him. The royal authority that she wields is completely dependent on her King allowing her to have that authority.
She's one of the original 6 Olympians, but if you compare her to her siblings she unavoidably falls short. Zeus, Poseidon, and Hades each rule over a huge chunk of the cosmos, and even though Zeus and Poseidon are terrible people who fail to live up to any ethical standards whatsoever, they can always fall back on being effective rulers and insanely powerful individuals. Demeter is singlehandedly responsible for keeping all life on earth alive, which she has never once failed at. Hestia keeps the hearth on Olympus burning perpetually, ensuring that the gods will always have a home to come back to no matter how much they fight, and Ancient Greek custom is that she receives the first offering at every household sacrifice to the gods. Furthermore, both Demeter and Hestia have a lot of overlap with the "motherhood" part of Hera's divine portfolio, while all three of the boys are rulers, so the only part that's exclusive to Hera is marriage, which simply does not have the same kind of intrinsic importance as what the other five do. Hera has by far the least important job of her siblings, and she can't even succeed at that.
She was considered by many to be the most beautiful goddess, but then Aphrodite came around. To add insult to injury, despite Aphrodite's MANY flaws, she's still more approachable and a better mother than Hera is.
If Hera were to suddenly disappear from the pantheon one day, all of her roles could be divvied up between Demeter, Hestia, Aphrodite, and Athena with zero issues. The only thing she really contributes to the pantheon is EVEN MORE drama and conflict: arguing with Zeus, targeting his various mistresses and children with undeserved wrath, and occasionally feuding with Aphrodite or another goddess. Consequently, she's even less popular among her fellow gods than Zeus is.
So eventually she takes a look at her life and realizes that she's a failure. In pursuit of being the Glorious Queen of the Gods and having a perfect marriage with perfect children, she's sacrificed everything -- her morals, her friends, her chance to have any power or worthwhile accomplishments outside of her connection to Zeus, her chance to have fun -- and she has nothing to show for it. All she has left is a husband who's worse than ever, children who by now are just as f***ed up as she is thanks to her and Zeus's awful parenting, a half-empty title of "Queen," a metric butt-ton of rage and hatred that she STILL can't point at its deserving target, and the faint hope that maybe one day Typhon will defeat Zeus and topple the world order and thereby free her from this living nightmare. Until and unless that happens, she's stuck, since she can't leave Zeus without being dragged back to him, she can't die due to being an immortal goddess, and she doesn't seem to be having new kids anymore.
The only recourse remaining to her is to go to Dionysus and get absolutely wasted so that she can temporarily forget how hollow and sad and joyless her life has become.