That is controlled by the ISP, the OnHub will have no power at all to reserve or keep the same IP. The OnHub will perform DHCP resolution based entirely on the settings specified by the DHCP server which is controlled by the ISP. Most commonly an ISP will charge an additional monthly fee for a static assigned IP address which will be permanent. Reserving a dynamic public IP is pretty much the same thing as having a static public IP and would likely cost extra just like a static. Some ISPs will purposefully set a very short lease time (minutes or hours) and configure their system to not give you the same public IP address so as to force their customers who want remote access to pay extra for a static IP address.
Different ISPs do things differently when it comes to dynamically assigned public IP addresses. My dynamic public IP hasn't changed in quite literally years but that doesn't mean it can't. Part of the trouble with dynamic addressing is that it might change frequently or nearly never and it may not do so consistently.
You can use any of the numerous
DDNS systems available to compensate for the changing public IP address. Some NVRs have the capacity to utilize DDNS and some do not. You can also run a DDNS software agent on a computer or certain routers can use DDNS as well.
DDNS or Dynamic Domain Name System (or server) is a service, often free of charge, to update a domain A record that points to your system. The DDNS uses a device on your network to call out to the service either at time intervals or when the public IP changes if it is running on your firewall/gateway.
After a google search of "DDNS" noip.com was one of the results so lets use that as an example. Lets say you register your noip.com account as 37tr3n5k and lets suppose noip.com makes an entry for you of 37tr3n5k.noip.com. If you have a time based agent running, say on a workstation behind the firewall so that agent can't know exactly when the public IP address changes so instead it runs every 5 minutes. Your current public IP is lets say 1.2.3.4 and it changes to 4.3.2.1, with a maximum cycle time of 5 minutes the A record of 37tr3n5k.noip.com resolves to 1.2.3.4 until it receives the scheduled periodic connection from your PC's agent software which shows your connection is now on 4.3.2.1 so the noip.com system updates its record and now 37tr3n5k.noip.com resolves to 4.3.2.1 until the next time it changes. Public IP address leases can be as short as minutes or as long as forever and anything in between. If your router/firewall can use DDNS that is often a good place to set it up since the router will know the instant a public IP address changes and so can update the noip.com system essentially in real time.
One of the reasons an ISP might be changing public IP address frequently is by having a short lease duration they can have more connections than they have public IP addresses
