So, many years ago when this site started, I needed a Dynamic DNS provider, and after some searching I decided to go with Sitelutions.com, and they continue to be an excellent provider of this service. Unfortunately, some months back they changed their policy on how low of a TTL (Time To Live) value could be set, this value controls when previously looked up data expires, and much be looked up again in order to stay current. I was in the process of upgrading my router, and as a result picked up a new IP address, and after encountering an issue had to switch back to my old router, using my old IP address. Unfortunately, I couldn't set a low enough TTL value via Sitelutions to keep up with these changes, and my site was effectively offline on the new router.
Some renewed searching led me to DNSexit.com, another free provider of this service, and they not only allow low TTL values (as low as 2 minutes), but actually encourage this for dynamic IPs.
They also provide Domain Name registration, hosting, and a variety of other services. I strongly recommend them.