If you come across an article older than 7 days and want to show your appreciation to the author leave a comment on the article. If author comments back, upvote their comment as a way to pay them.
I too like the idea of leaving rewards open past 7 days but there are some negatives to that should be addressed. Leaving rewards open past 7 days could cause a lot of spam rewards. It would also complicate the checks and balances we currently have on posts. Currently you can upvote a post til 6 days and 12 hours but after that it is downvote only; they do this so that people can't upvote their things @ 6 days 23 hours 50 mins and steal a huge reward. The 12 hour downvote rule gives time for community regulation on shit posts. There are people that watch the expiring posts with high value for content.