ISPs, including Verizon, typically set a time limit on an IP lease after which the modem will automatically and invisibly to you request and receive a new IP lease. When your network is up and running 24x385 it is not uncommon that in effect you renew the lease on the same external IP address, but that is NOT guaranteed. By-the-way your local router typically uses the same dynamic (leased) internal IP address scheme for your Local Area Network.
So to summarize there is no benefit to be gained by restarting the modem to lease a new IP address or renew the lease on the same IP address you already had. The ISP does a more than adequate job of taking care of itself and NAT does a decent job of shielding your computer from outside malefactors.
