The whole point of the weekly challenge is to get people to go out that week and take photos on the subject posted. Using past images defeats the whole object of the challenge.
That's where it goes wrong, I thought the whole point of the exercise was to take pictures, not to force you to go out with the camera. When you have a busy schedule you may not be able to go out on a weekly basis and having that imposition of planning a weekly outing with the camera, combined with looking for a shot to satisfy a brief, it's easy to think I'll miss this week's competition, which then becomes next week's as well and the week after that ad infinitum, hence the low turnout each week.
Just a point re the imposition of a brief or theme. Our club was bequeathed a trophy to be presented annually for the best print on a set theme. Initially the number of entries was quite high, after all you had a year's notice of the theme/brief. Entry numbers began to dwindle and over the last three years entry numbers have been 4, 4, and this year 2, from a membership of 150. When put to the members why numbers were so low the resounding reply was that they didn't like the imposition of a brief. When pushed further as to why they disliked a brief being imposed, it seemed they felt restricted as to what they took and usually the competition ended up with a succession of images that were no too different from each other.
I would hazard a guess that a monthly competition for the best image you have taken within that month would attract more entries than the current set up. Tell me which dot to fill in within the vote and I'll dot it in!