The comforts, traumas and shortcomings of “Memory” make for a poignant if somewhat melodramatic romance and star vehicle for two of the best in the acting business — Jessica Chastain and Peter Sarsgaard.

It’s a story of two damaged people, lost in different ways — one grasping for memories worth keeping, the other trying to grapple with what she can’t forget, and move on.

We meet Sylvia in a filmically familiar space — the dimly-lit church basement of big city Alcoholics Anonymous meeting.

She is 13 years sober. It’s worth celebrating. So she’s brought her teen (ish) daughter Anna with her, because that’s the nature of their relationship. But while Anna knows about the drinking, she doesn’t know when and how it started.

Sylvia works in an adult special needs home, which takes a special kind of caring. But she isn’t just wary about men. She’s alarmed, alert and determined to keep her distance from them.

The fridge breaks in her apartment, and the repairman buzzes the intercom.

“I asked for a repair WOMAN,” she snaps.

Then there’s this fellow she glimpses at a high school reunion. She notices he’s behind her as she heads to the train. She keeps her distance in her car on the El. And when he trails her all the way to her apartment, she’s almost alarmed. She recognizes him.

But when he stays out there in the rain and sleeps in it until the morning, Sylvia picks up on something. Being in the social service system, she knows who to call.

Saul, it turns out, has dementia. His brother (Josh Charles) and niece (Elsie Fisher) live with him as caregivers. After she stops by to see Saul, they wonder, might Sylvia be available to pitch in?

But they didn’t hear her conversation with him. They don’t have a clue of their “connection.”

The latest film from the writer-director of the Tim Roth star vehicles “Sundown” and “Chronic” struggles to not tumble into Lifetime Original Movie territory. One plot twist snaps your head back. Another makes you scratch that same head because you, like everybody else, thought we’d moved past “all people with major mental health issues really need is love” pablum.

The latter half of the second act has some eye-rolling leaps of logic that almost took me out of Michel Franco’s movie.

But Merrit Wever of “Nurse Jackie” brings a touch of Earth Mama flintiness to the role of Sylvia’s happily-married with kids younger sister, Olivia. Charles gives his brother-of-the-demented-Saul role some edge. Jessica Harper, playing the mother of Olivia and Sylvia who may know the origin story of all this hurt, or at least help clarify it, maintains an aloofness that tells us she long ago made up her mind about Sylvia’s “problems.”

And the leads are pretty much flawless. Chastain lets us see damage that cuts so deep it may make Sylvia an unreliable witness to her own trauma as she over-compensates as a protector and nurturer. Sarsgaard gives us a man whose short-term memory is almost completely shot, but who has taken that as an excuse to “live in the moment.”

It’s never that “cute,” to its credit.

But whatever lapses “Memory” suffers from, these two ensure that it is never less than engrossing, and that their characters connect in ways that can’t help but be touching, even if “far fetched” comes to mind as they do.

Rating: R for some sexual content, language and graphic nudity.

Cast: Jessica Chastain, Peter Sarsgaard, Brooke Timber, Merritt Wever, Jessica Harper and Josh Charles.

Credits:Scripted and directed by Michel Franco. A Ketchup Entertainment/Mubi release.

Running time: 1:40