DHCP leases expire 24 hours from the time they are issued and automatically attempt renewal starting at 50% remaining lease time. This process does not cause any disruption of service or any other side effects noticeable to the customer. The only time you'll see any issues is if there is a failure.
DHCP renewals are usually something that doesn't impact your connection - it isn't like your modem actually disconnects and reconnects. Basically all it does is ask if it still should use the same IP address. I've only seen an issue when the IP address changes, certain sessions will disconnect and need to be re-established in that case.