This sounds just like a real unfortunate issue only because that was the only (or last) flight to Belize.
It's easy for us to say that 40 minutes isn't the best option when we are aware of how everything works. But I know for sure, if I was just a casual flyer and went online, and United/Kayak/whatever comes back with a set of flights that make my wallet happy, and I have a 40 minute connection time - I'm happy and not going to think anything of it. Most likely if there was another flight, this would have ended better.
And to whomever made the comment about equating this to a job interview- thats a terrible example. If i was driving to a parking garage, I could leave anytime I wanted. I would have to factor in time to clean my car, sure, but I can account for this. If I have to be somewhere by 10am, its not like I can only leave at 9am. If I'm not there at 10am, thats my fault. Ill leave at 830. But when I need to be on a MSP-IAH flight that doesnt run whenever I leave my house, and the United website says that I can do this, I'm going to do this.
Sorry OP, hope you get something in return.