Is there a method to automatically start an application, or restart an application after x seconds? I'm hoping there's a 3rd party application that does something like this.
There is application called "Sleep" via Cydia, this application will make your iPhone repring after configurable period of time. After repring, only "Mail" & "Phone" are remain running, all other applications will be terminated.
Of course you will need to jailbreak your iPhone to get this application.
You could create a webpage that launches the app and have the page refresh every x seconds. To restart it, you could have the page launch another app, which would kill the first app, then launch the first one again.
You could also port cron to the iphone (i wish someone would) and control the app with a bash script.
ETA: sorry, cron is apparently already on the iphone, but it is apparently unusable with iphone apps