I would start by assuming it will naturally take them more than one week to completely fix this problem, and ask if the fault is so severe that it would be bett

I would start by assuming it will naturally take them more than one week to completely fix this problem, and ask if the fault is so severe that it would be better to take the service down until it's fixed, both from the company's viewpoint, and that of an external entity able to force it being taken down even if it kills the company. If the answer is no to both, it's not that dire and they can be given 3 more weeks, precipitate action would not seem to be required. As for deadlines, experience shows they are so frequently required that you will need to set one; there's a lot that's been written about this so I'd look for that.