Can't speak to recently but it used to happen all the time. There were multiple flights VIPR decided I would not be able to make that I ended up making and having to fight for a spot at the gate (often times being moved from F or C+ into a seat in the very back of the plane..).

Maybe they've gotten better about it. It absolutely used to be that if your arrival time violated minimum connection time rules they would so very helpfully rebook you to another flight.

I distinctly remember (admittedly several years ago) a connection in JFK (I think from Dublin). Non-Canadian per-clearance I-D minimum connection time is 1 hour for some reasons (rather than treating it like a domestic flight). I had something like a 1h5m connection time. Unfortunately the MCT for DUB-JFK is 1 hour (even though it is per-clearance). While in the air my flight got like a 25 minute delay estimated, so I would arrive with 40 minutes to connect. I was "helpfully" rebooked on a flight two hours later (with no seat assigned). We ended up getting to the gate around 15 minutes late leaving me 50 minutes to connect.

My departure gate was... two gates down in B. I literally got to the gate ten minutes before they even started boarding. All the gate agent could do was put me on standby. I lost my F upgrade (I had used a GUC for the whole route) and ended up in a middle seat in the last row of the plane. It was definitely the Delta Difference that day.