Most consumer level battery backups don't last very long (average 15 - 20 minutes, more the less power you actually use). If your power goes out for a couple hours your probably going to run out of battery power even if the modem/router is the only thing on the UPS.
Besides, your ISP can reset your IP whenever they please. It might only happen every 6 months, but are you going to notice the change immediately and be able to update your DNS immediately? It will likely change at the least convenient time, like when your out on a trip for 2 weeks or your at some hotties house and want to show her your kickass site.
I think you're better off doing the dynamic DNS thing, unless you don't really give a shit if your site is up or not. It also doesn't cost you anything. It still wouldn't hurt to put your modem/router and server on a UPS anyway though.
Looking at ZoneEdit again though, I can't see any place where it says it does dynamic DNS. I'm was sure I saw it before, but maybe my mind is playing tricks on me. One thing you can do though, is use DynDNS.org (
http://www.dyndns.org/services/dns/dyndns/) to handle your IP changes. That will give you a static host name. Then you can use ZoneEdit's WebForward feature to point to your static host name. The domain is cloaked, so no one going to your site will know the difference. I used to do this with adamo.org and run my own web/mail/ftp services. It's all free.
Is webhosting with a dynamic IP address possible?
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