Why after 4 hours does my iphone 5 say called failed?

The "call failed" message means that your iPhone lost communications to the cell tower network. There are many possible causes for this. It could be that your battery is getting too low to keep the connection alive. It could be that the radio is overheating from being on for such a long period and it is failing to work within specs. It could be that your ell provider has something set in their towers thinking that it is an error when a call lasts that long, and they "fail" the call to prevent tieing up resources on dropped calls that didn't disconnect on your end. We would need more details to try to narrow down the probelms for you.

A number of years ago I was on a 2 hour cell call for work support overnight. About 45 min-an hour into the call my cell gave me a low battery indicator so I connected the AC power and contiued the call. At about 2 hours in, the phone got too hot and it just turned itself off dropping the call in the middle. At that time, it was a phone issue, but cell phones weren't designed to be used for 2+ hour calls then, so I don;t know of any cell phone that would have done better.

To be honest, I'm not sure why you are using an iPhone for 4 hour long calls now. There are so many better options.