Fifty minutes is plenty of time to connect in Denver if your incoming flight is on time. I'd go so far as to say 30 minutes is enough time if you walk quickly...the United gates aren't all that far apart.

If you miss your flight due to late arrival, UA will re-book you on the next available flight, no cost or penalties. Key word here is "available". That could be same day or next day, depends upon how full the flights are that day on that route and, of course, the schedule.