Useful to know the lease time (which I later saw in the Hub's pages too) - I've been used to BT's DHCP policy where a Hub usually gets a new IP address from the pool at random on reboot - pros and cons to each.
It would have been an 'issue' with a rogue machine, like I apparently had, jumping around to different IP addresses and thereby circumventing the blacklisting for a while....
Too put it is easy terms, when you device is turned it sends the hardware ID to the DHCP server that gives out the IP address, the DHCP server will check that hardware ID with it database to see if it has had a lease given out before, if it has and the IP address has not been taken by a new device you will get the same IP address if it has been taken you will get the next free one.
My lease changed around 2.5 years ago when virginmedia segmented my local network, but since then I have had the same one, mostly because I keep my hub and router turned on, even when I had no kit on for over 1 week still got the same lease this happened beginning of October.
So although they can change it is rare unless the network has been segmented or a new user picks up your expired lease when you device is off.
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For what it's worth, Hola VPN doesn't exactly have a stellar reputation among Internet Security specialists, partly because there have been numerous reports of the installer apparently also adding a nice batch of malware products and also the nature of how it works. It basically sets up a big P2P routing network so your traffic can be sent out through someone else's connection to bypass Geo blocks, but that does imply that other people are accessing the internet through your connection - and you have no real way of knowing what they are doing on it.
Earlier versions of the app also had really bad security vulnerabilities, was leaking personal user data all of the place and there were stories that the originator of the code were selling off customer IP address to anyone interested.
Personally I wouldn't touch it with someone else's barge pole!