'out of sight, out of mind' is generally applied to things and problems, not, say, warm relationships.
Really? I've seen it used twice for non-relationship contexts, but too many times to care to count (on the order of 50-80) in the context of long-distance relationships, usually as a warning that a couple should not hope to remain steady and trust eachother if they become far apart for a long period of time (months or more) for the first time since entering a relationship.
In fiction, this either turns into a self-fulfilling prophecy or becomes the whole reason the main character can complete the main quest.
In reality, the causal influence doesn't seem to be there, but anecdotally I observe that the drifting-apart usually happens regardless of whether any such prediction was made. Knowledge of this leads a significant fraction of couples to break-up preemptively when they're about to enter such a situation.
That's interesting. I'd more seen it used with annoyances. Maybe because I haven't seen much of LD relationships, and those that I did see, worked. And it was clear they were going to work from the outset because they were really serious about each other.
Absence diminishes weak passions and increases great ones, as the wind blows out candles and fans fire.
Here's the new thread for posting quotes, with the usual rules: