Actual check-in cannot be done via kiosk after a certain point: 60 minutes for international and I think 30 minutes for domestic (just talking about check-in, not checked baggage acceptance which often ends sooner). If you already successfully checked in, IME, reprints can be done anytime via kiosk or agent (perhaps not once boarding has begun).

It sounds like what happened is that you arrived at the airport knowing about a delay, but close to the ORIGINAL, SCHEDULED departure time. In case you didn't know, the check-in deadlines are based on the ORIGINAL, SCHEDULED departure times, not delayed/actual times. I have run into this problem overseas in the days before OLCI was allowed on international itineraries. If you check online and it says your flight is delayed 3 hours, of course you would rather stay in the city a bit longer. But you still need to check in by the ORIGINAL check-in deadline, which is 60 minutes for international and 30 minutes for domestic, UNLESS you are checking bags, in which case if varies by station...I think MIA is 45 minutes for domestic baggage acceptance.

Even with a delay, 47 minutes is cutting it WAY too close at MIA. What if there had been crazy TSA lines (if you had not been granted PreCheck, or if the PreCheck line was not operating)? I recommend 1.5 hours for domestic and 2.5 hours for international. Better to be safe than sorry. And that way, you get to enjoy the ACs and/or OW Premium Lounge for a bit longer!