The only possible issue I can see with just using one week to record attendance is that you could easily miss people who missed a week. I can't really think of a good way around that other than to perhaps collect attendance sheets from small group leaders and have someone do a Post-Attendance on the small groups.
That's relatively easy to do, but if you have a large number of small-groups, it would get quite time-consuming. The
good thing is that you can easily pull up a list of people assigned to the group and record attendance for existing members without too much trouble. New members would take a little longer, but would still be manageable.
Giving this to your small group leaders makes the most sense, but I can see that getting buy-in would be difficult as it would be a new process to follow and there would be some training required. I feel that the benefits are high, though. It's easy to know that John hasn't shown up in "a while", but a lot better to know that he really hasn't shown up for the last 4 weeks. Has anyone checked on him in that time? Is he okay? Maybe your groups do well keeping track of those sorts of things already, but from experience, it's easy to just figure that he may have gone out of town or been sick and will be back "next time". Meanwhile, next time turns into quite a long time and John feels like nobody cared enough to check on him. He's moved on to another small group or perhaps just stopped going altogether.
If you have a manageable number, you may want to try this with them to see what you can work with. Perhaps starting with a couple of "pilot" small groups and building up from there would help others to see that it's not hard to do and has benefits beyond just plugging numbers into the system.
In Him,
-Peter