Batman's problems in Gotham can't be solved as easily as calling the Justice League. For many, it's perplexing to see Batman carrying out DC's quintessential super-team is a distress call away, that should presumably fix all the city's problems in one fell swoop.
Batman: Dark Age #5 by Mark Russell and Michael Allred goes a long way to reiterate how and why the Justice League cannot be the Dark Knight's - or any superhero's - one-stop shop to solve their own personal problems. Batman comes to the League pleading with his friends for help in Gotham, and because there are more pressing matters at hand, the Justice League is forced to turn their friend down.
Multiple cities in the DC Universe are forced to take a backseat to the Justice League's affairs because Justice League affairs are galaxy-wide, and they can't put their focus on just one city on Earth.
The Justice League Tells Batman They Can't Save Gotham - It's Too Small
Batman: Dark Ages #5 by Mark Russell, Michael Allred, Laura Allred, and Dave Sharpe
By the the fifth issue of Batman: Dark Age, the Caped Crusader has been put through the wringer in a conflict with Ra's al Ghul. In this universe, Batman's feud with Ra's led the latter to burn down Arkham Asylum - fear he couldn't beat him, but nearly put down his cowl over the ordeal.
His last resort to save Gotham City was to go to the Justice League for help. In the Hall of Justice, Batman addresses the League, expressing his grievances and concerns about Ra's Al Ghul, and practically begs for their help to save Gotham City. However, his call to action falls on distracted ears, not necessarily due to lack of interest from any of the heroes, but because something much bigger transpired while Batman was away and focusing on Gotham.

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After speaking to Brainiac, the Justice League now knows that the Anti-Monitor is about to drain the entire universe into antimatter. But before that happens, Brainiac plans to strip the Earth of its biosphere. In short, the Justice League has bigger things to worry about, problems that affect the entire galaxy, and they don't have time to focus on just one city on one planet. Batman's concerns about Gotham have to wait, and if he can't wait, then he is on his own to fend for Gotham by himself.
Gotham Isn't the Only City Left Behind by the Justice League
Just Ask Black Lightning in the Suicide Slums
Gotham City isn't the first city in the DC Universe that can't have the Justice League's undivided attention, and it probably won't be the last. Another example comes in the form of Metropolis' Suicide Slums, now rebranded as the Southside Heights neighborhood. Readers familiar with Jefferson Pierce will recall that a major reason why he became Black Lightning is because Suicide Slums was once the area of Metropolis that all the superheroes ignored, including the Justice League.
Black Lightning is currently starring in his own miniseries as part of DC All In. Check out Black Lightning #1 by Brandon Thomas, Fico Ossio, Ulises Arreola, and Lucas Gattoni, available now from DC Comics.
While there is obviously more to Black Lightning's origin story than that, the fact of the matter is that the Justice League failed the Suicide Slums. At a time when crime was rampant in the neighborhood, superheroes ed over the area every time. However, like with Batman, it wasn't a personal dismissal - it's just that there are always more pressing, often Crisi-level problems elsewhere. Metropolis itself is rampant with Superman's rogues gallery, a group filled with intergalactic threats that will always take precedence over the street villains within the Slums.
The Justice League Is an Intergalactic Super-Team, Not a City-Wide Task Force
Batman Learned Their Priorities the Hard Way
There's a reason why Metropolis matters are solely Superman's responsibility - until a potentially global threat shows up, like Doomsday, that is. There's a reason why the Flash Family takes care of matters in Central City, while the Justice League doesn't have a presence there. And backtracking to earlier, that's why Black Lightning makes the Suicide Slums his responsibility, despite it being a neighborhood within Metropolis. Even Metropolis is too big for Superman to handle the entirety of it by himself, but all the other League heroes are also busy taking care of their own cities when they're not dealing with League business.
The Justice League needs to first prioritize the biggest threats that affect everyone in the universe.
Batman surmises it best when he says that trying to compare his Gotham problems to the intergalactic crisis at hand was like "a man in a burning house trying to blow out a candle." As big as they are as a unit, the Justice League can't be in more than one place at once. It's not a matter of neglect but more of a matter of time and effort without risking drainage. The Justice League needs to first prioritize the biggest threats that affect everyone in the universe, so if that means putting Batman's Gotham on the back burner, then so be it.
Batman: Dark Age #5 is available now from DC Comics.