Liam Neeson turns 70 next month, and one review of his latest shoot-’em-up, “Memory,” carries the headline, “Getting Too Old For This.” While this presumably refers to the actor, one can’t help but wonder if the same doesn’t apply to the movie’s audience. At what point does cinematic fiction impinge upon not only genre expectations, but the viewer’s maturity? 

Mr. Neeson’s transformation from period-drama mainstay and man of the stage to full-throttle action hero is among the quirkier career trajectories. Beginning with “Taken” (2010) — a considerable hit that surprised its star, who thought the film was heading straight-to-video — Mr. Neeson has been cranking out one interchangeable tough-justice picture after another. The box office demands them and the star is happy to oblige.

This latest venture seemed to promise something different. “Memory” is the American version of “The Alzheimer Case,” a 2003 Belgian film based on a book by Jef Geeraerts. Given these sources, “Memory” had the potential to play off, and perhaps expand upon, Mr. Neeson’s status as a movie star of a certain age. It’s not too many minutes into the film before we realize that pulp hyperbole will take precedence over the more mundane contingencies of getting old.

We shouldn’t necessarily expect verisimilitude from a rock ’em, sock ’em thriller. Still, “Memory” does begin in a manner that is simultaneously outlandish and somewhat grounded. We meet Mr. Neeson’s character, contract killer Alan Lewis, just as he pulls off an immaculately staged hit. Climbing into the getaway car, Lewis reaches for the key; it isn’t in its usual location. Hesitation and doubt cloud Lewis’s face. Things aren’t altogether right.

Lewis has been covering for his lapses in memory by scrawling notes on his forearm and taking medication for Alzheimer’s disease. He’s ready to call it quits — until an offer comes along that can’t be refused. Lewis only partially fulfills the job because he discovers that one of his targets is a teenage girl. The consummate killing machine draws the line at children. Honor amongst thieves, and all that.

The plot weaves its tangled web in El Paso, Texas. Lewis crosses paths with a cadre of sex traffickers based in Mexico. An FBI team headed by Vincent Serra (Guy Pearce) is working undercover trying to stem the tide of child prostitution. Then there’s Davana Sealman (Monica Bellucci), a real estate mogul who appears to be channeling the ghost of Elizabeth Báthory. She has her fingers in a little bit of everything, not least the local government.

Anyone with a friend or family member who has suffered from Alzheimer’s will find much in Mr. Neeson’s performance that rings true — at least, in the early sections of “Memory.” A niggling sense of unease and puzzlement filters through Lewis’s actions. Mr. Neeson embodies this hapless estrangement to pointed effect. That his character continues to bash heads with almost musical precision doesn’t prevent a certain poignancy from setting in.

Somewhere along the second act, “Memory” goes gonzo. Whatever credulity that’s been established is stretched to Silly Putty-like extremes once Lewis taps into his inner-Rambo. It doesn’t help that Martin Campbell, who did much to invigorate the James Bond franchise with “Casino Royale” (2006), directs with little sense of having a personal stake in the proceedings; his work is swift but pedestrian.

In the end, this isn’t Mr. Neeson’s movie. “Memory” belongs to Mr. Pearce. Coming across like Brad Pitt after having been put through the wringer, he takes charge of the movie, inhabiting his perpetually frustrated FBI agent with grit-under-the-fingernails vigor. Many of us first took notice of Mr. Pearce in “Memento” (2000), another — and better — movie about the fallibility of memory. That he’s a co-star here is a purposeful and unfortunate irony, and puts into high relief the shortcomings of “Memory.”