I think, follow up your email with a phone call, to make CERTAIN someone knows, NOW.
Like I said, this situation quite often has been mentioned on the forum. It all depends how far they have actually gone with someone's case - sometimes, if there has not been any hassle, they may have done more of the procedures than they have told the applicant about, so when the 'I've only got x weeks' call comes, it's only a matter of the last formalities, and the Residence visa is issued very quickly. But if they are still waiting for a reply on some verification(s), then they will need to say to get another work visa.