I guess, we are talking about public ip addresses from the ISP.
Most ISPs will give you a new ip address on disconnect and reconnecting.
Changing internal ip addresses makes absolutely no sense. The standard lease time of 3 days is ok, espacially when a pc is corrupt and will be substituted.
Again, I misread the OP. Thanks Paul, upon rereading it carefully I see that's what he's talking about alright.
*slapping self on forehead*
For what it's worth, the customer doesn't control the ISP's lease times. I don't even know what my lease time is for my ADSL here at home. All I know is the MAC of whatever is connected to the modem controls my IP. If I change the MAC, I get a new IP. Otherwise, I don't. I've had the same IP for a couple years now.
Conversely, my best friend back home has ADSL from another provider (of course - he lives over 400 miles away right) has a setup wherein his IP changes constantly throughout the day, even if he never powers off his PC or changes anything.
I know why his ISP does that. It prevents people from running websites from home, or P-to-P software, if they don't know about the online proxy's and dynamice DNS that's available.
I will say, it's particularly annoying when we're trying to game because I've literally seen his IP change 30 seconds after he just looked at it on 'whatsmyip'. I think their lease time is like 10 minutes.