Rule to check specific field of content every week
A possible solution is to transform the rule you already have, into a Rules Component, so that your original Rule "schedules the execution" (using the Rules Scheduler submodule) of that Rules Component (eg X secs or mins "after saving the content") ... That Rules Component will then be executed next time cron runs.

If you then also add an extra Rules Action in that Rules Component (as last Rules Action) to reschedule the same Rules Component after 1 week, you should have achieved what your question is about.

Obviously, as soon as at least 1 of the Rules Conditions in your Rules Component are no longer satisfied, its Rules Actions will not be performed anymore, so that is when the weekly rescheduling also stops.

Easy, no?