I wouldn't close the account. Just pay it off if you have a balance and put the card away. Closing long-time cc accounts may negatively impact your credit score, while keeping it open, but with a zero balance, will help your score.
I'm also assuming that at some point, once they see that long-time cc customers are no longer using their cards, they WILL be sending out some kind of coupons or rewards or SOMETHING to get people back in the store. If they do, THEN you can go and make a small purchase, pay it off, and then put your card away again.
This new model of business may not work for them, and if they lose enough business, I am sure they will re-evaluate what they are doing. So this might last a year, two years? Who knows?

Hopefully people will only purchase items that are a great price, not just so-so...