This question relates to someone you consider a friend (not an “acquaintance”), but not a really, really close, easy, give-and-take, we’ve-seen-each-other-in-our-underwear friend. But this is a friend you’ve done plenty of things with and you clearly enjoy each other’s company. It is a friend of the opposite sex, but not a romantic relationship. (And yes, we’re both kind of fussy.)
MAIN QUESTION: If you invite this person to do something (lunch, movie, coffee) and they can’t go at that time because of work and they say, “I’d like a rain check,” then is it up to them to issue the next invitation? Or is it okay and good etiquette/protocol for you to issue another invitation to do something before they have “redeemed” their rain check?
NOTE: You’re sure they had a good reason why they couldn’t make it- IOW the “rain check” request isn’t just a way of putting you off. I’m saying this because I’m anticipating responses like, “If this person is such a good friend, you shouldn’t have to stand on ceremony,” which is a good answer, but not the information I’m seeking.
Some people like the idiom “rain check” and use it often. Other people don’t use the idiom. You can’t derive much info from that alone.
I’d interpret the message from your friend as simply “I approve of the activity and would like to do it as a general matter, but not at that particular time.” So the point for you is “Don’t mistakenly assume I’m sending a “message” that you should cross that activity off the list of things we might do together.” Nothing more.
The idea there’s some tit-for-tat obligation or ritual that you both need to alternate offering and accepting is 100% silly.
I have friends who almost never offer an event but accept most of the offers I make. And vice versa. I don’t see either of those arrangements as impolite, unacceptable, or uncommon.
First: Do you mean “invite” as: I invite you so I pay the bill for you (and therefore taking turns is important)
or do you mean invite as: Let’s get together, and we pay dutch? (so taking turns is not important)?
Second: I would ask right at the moment when the person gives you the rain check. You ask your friend “Can we meet on Thursday 6 pm”, and they say “I’ll have to work late, I’ll take a rain check”, your answer should be “So when would be a good next time?” If they are busy for the whole fortnight, they’ll say “I’ll call you when I’m free”; if they are only busy for Thursday, they’ll say “Give me a call when it suits you”.