Static IPs are becoming very rare with any broadband company, as they are difficult to manage, require more work... and plainly speaking, they're not common anymore.
Dynamic IP addresses, in the sense of DSL or broadband, usually don't change all that often. You may want to check your lease time to see what it is.
As far as being disconnected...
When an IP lease renewal occurs, you won't be disconnected, even if in a file transfer. After the address renews, the gateway is reopened, and any windows based operating system should be able to reconnect anything it was doing, as when it finds no connection, it will attempt to make several requests for a few seconds, if this is not happening for you, you may want to adjust the timeout in your software.