Wikipedia on Suspicious Minds explains:
Elvis' primary producer Felton Jarvis made the unusual decision to add a premature fade-out to the song starting at 3:36 and lasting for 15 seconds before fading back in. The first verse then continues repeatedly until it completely fades out. In a 2012 interview with Marc Myers of The Wall Street Journal, Moman disclosed that Jarvis was never happy with Elvis recording at American Sound Studio, saying "it was a control thing." Moman added, "So when Jarvis took the tape of 'Suspicious Minds,' he added this crazy 15-second fade toward the end, like the song was ending, and brought it back by overdubbing to extend it. I have no idea why he did that, but he messed it up. It was like a scar. None of which mattered. Soon after the song was released, Elvis was back on top of the charts."
I find it quite an interesting resource, but also disconcerting, that I have never listened in other songs.
There are quite a lot of resources explaining the why of the usage of the resource in this song, but I cannot find explanations on whether this was used anytime before Felton Jarvis did.
Was Elvis Presley's 'Suspcious Minds' the first song with a fade-out and fade back in?