"a long memory for" is a perfectly valid and usable phrase in written English.
You can use it when you are referring to someone's ability to remember details or facts for a long period of time. For example: "My grandmother has a long memory for birthdays and anniversaries."
He had a long memory for injustice.
He has a long memory for the cuts of snobbery.
Last season he cut loose as Ferrando, a superstitious captain of the guard with a long memory for dark doings, in David McVicar's new production of Verdi's "Trovatore".
The eldest son of a wastrel father, who abandoned his young family the moment his wife died, Robespierre was a sensitive, serious boy, with a long memory for personal slights and a fierce compassion for the vulnerable.
That is, she has a long memory for pre-war and pre-First World War service; and thinks nothing of calling the American ambassador if there's no toilet-paper on the train etc.
A former -- and unsuccessful -- theater director, he is volatile of temper, has a long memory for a grudge and employs a small army of ex-K.G.B. men who are notoriously tough in the service of their master.
The tape was an outtake, clipped from a moment of horseplay after he taped an ad as a Republican, and someone with a long memory unearthed it for the House Republicans' campaign committee.
Chang et al. (2012) examined a long memory volatility model for 16 agricultural commodity futures.
This information is likely to be used to persuade or play mind games with you at a later date (they have a very long memory for information discovered on such fishing expeditions).
But Brussels has a long memory and knows that calls for economic government in Europe are not really new at all.
"It was only bad management that lost the war," said Henry Stimler, an Englishman with a long memory who has been in New York for only eight months, "They wanted to be British.
