Montag remembered Faber after so long because he offered him one of the first opportunities to hold a true conversation with another human being. When Montag first sees Faber in the park, he notices that Faber is trying to hide something in his coat. What begins as a psuedo-interrogation devolves into a real, natural conversation. They sit together for an hour, and Faber quotes some poetry, which sparks Montag's interest. When Montag goes to leave, Faber gives him his address, which Montag keeps until he visits Faber later in the novel.
This incident made such an impact on Montag because he is so lonely and isolated in his world. His wife Mildred makes no attempt to have a true relationship with him...or anyone else really. Until Clarisse McClellan comes along, Montag has no one to call a friend, and no one with whom to share his thoughts and concerns. Because Faber offered him that, however briefly, he remembers it later when he is under such stress.