In Computer Science, in some protocols, there's something called "exponential backoff" when something would otherwise break.
When you have a problem with someone else, I recommend exponential backoff. First time you annoy someone, go away for 1 unit of time. Next time, 2 units. Then 4 units. Etc etc etc.
I've found, looking back on my experiences, that's how I handle people a lot of the time. Back off in larger increments each time. Persistence is important in some things, yes, but giving people more time each time does help, I find.
It's not simply that x time has elapsed since you pissed someone off, it's that it's been y units of time since you last tried to talk to them about it.
Golly gee I'm a dork.