Buried beneath a shlubby wardrobe and a sulky demeanor, Catherine Keener drags herself through “War Story” like one of those exhausted mothers in a missing-child movie. What her character has lost, though, isn’t her offspring — it’s her marbles.

As Lee, a traumatized American photographer who has taken refuge in a Sicilian hotel after a harrowing trip to Libya, the doughty Keener is rarely out of our sight. Baggy-eyed and ashen-faced, Lee turns her room into a bunker, licking her wounds and ignoring her incessantly ringing phone. Why she doesn’t just turn it off is only one of this film’s many annoyances.

Aiming for a moody portrait of psychological distress, Mark Jackson directs with a sluggish pace, an abstract style and a dismal aesthetic that rebuff involvement. Releasing information in stingy dribbles, he shadows his tormented heroine as she creeps around the hotel and loiters near a Muslim detainment camp.

Things brighten (at least for anyone who enjoys an actual story) when she becomes involved with a pregnant Tunisian migrant (Hafsia Herzi) who’s desperate to escape both Italy and motherhood. But whenever the script comes close to touching on anything interesting — like Italy’s treatment of immigrants — it shies away to pursue yet another of Lee’s mopey walkabouts.

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It’s all quite trying. By the time Ben Kingsley, playing Lee’s mentor and former lover, pops up momentarily to note that she’s a little nutty, it’s too late. That’s one of the few things we already know.