Iphone likes to shut down on its own when handled

For the last week my iphone has got a mind of its own and like to try to shut down on its own. Sometimes it would give me the red button+slide to turn off...sometimes it just goes to the Apple logo then shuts down.

No hacks on it, maybe two apps max like ebay so really nothing that would point out to an issue. This is also a replacement my original phone had a screen issue this summer where you could not touch anything else than the bottom bar. I swapped it for this one so it is virtually new.

Not sure if it is the button on the top that is stuck and it does not look like it.

Any similar experiences? I heard other users had issues with their iphone shutting down for no reason.