In my experience this is likely to be an issue with the software, either a bad app update, or the operating system.
This calls out no check ins from SpringBoard. SpringBoard is the process that runs the home screen. It could be an issue with hardware, but if the panic is always the same, my guess is that it's not.
What I would try is, if you haven't done so already, is to [guide|133851|put the phone in recovery mode|new_window=true] (or DFU mode, but that's not usually needed), and do a reset using iTunes. People say hard reset and mean a lot of things, so I am just clarifying that this is what usually fixes in my experience.
Set up the device without restoring any of your backups and see if that helps. Restoring information from a backup, or with data from iCloud can reintroduce the problem, so I would want to be sure it's a totally clean install and see if that works rather than loading potentially bad data back into the phone.