This 'instant' disconnection seems to be the general way some ISP's work nowadays.Especially if you want to cancel their service. Most of the customer service staff use a on-screen advisor, which can cause problems for both the customer and the service staff. Not right by any means, but that is the way things can turn out.
I changed from dial-up to broadband, using the same ISP,and I was assured that no interruption of service would occur. It did,with two days break between re-connection. The ISP didn't have a logical answer, when I contacted them.