I had this exact problem with my brand new Traeger Ironwood 650 when I bought it last week, my iOS app would reset every time I tried to enter the nickname for the controller and jump back to the start of the WiFire setup screen. The controller on the grill would show it connected to my home internet and my router confirmed it, but the app connection was a no-go. The controller showed an out of date firmware and it would not download or install the current version. Calling Traeger they said they were "well aware" of it and working on a solution but couldn't give me any more information or timeline than that.
There was a post about this on the Traeger Reddit forum and when I posted my issue there a Traeger employee who frequents the forum contacted me privately by direct message. He is not in support (I assume he works in development) and asked me not to publicly share his name because he can't be inundated with requests but he stated he knew the exact issue I was having and that the development team was likely going to send out a fix last weekend to all grills to stop this from happening but in the meanwhile I was able to provide him my grill serial number and he "pushed" a special fix to my grill that immediately got my app to see the grill, I didn't even need to setup the app, it seems they did it on their end, the WiFire tab was just automatically working without having to do the setup process. The only thing I had to do is open the "nickname" tab and change it to my desired nickname because they gave it a generic nickname like "Traeger" or something. The app has some bugs in it (couldn't change temp only see the temp, couldn't turn on super smoke etc.) until the grill updated to the current firmware (my grill was on 1.0.0.1 vs. I think the current 1.0.0.4?) in the next few hours and then the app worked perfectly.
The bottom line is this... this issue is FIXABLE WITHOUT having to get a new controller. Traeger DOES have a way to fix you remotely RIGHT NOW but is not communicating that properly to their customer support team because apparently the developers are creating a global fix as opposed to a one by one "push fix" that setups each grill on their end rather than you setting it up on your end. It's NOT a good first experience with the grill but the bottom line is this is software and hopefully everyone gets fixed soon.