Most junior days son was invited to he could not go because of baseball committment, baseball begins here (or at that time) early february. He did call and said thank you and explained, I agree that has to be done. Also being where we are situated so far south in florida, it takes 7 hours to even get out of our state. That meant a 2-3 day trip, and it becomes costly and coaches understand that. In fact, most liked the fact that he honored his team commitments. He did go to one that was close to our home, with at least 50 in attendance. It was first junior day of two for the weekend.
Some schools make it an event and others keep the numbers down. IMO, most of the time you are just a potential prospect.
I do not beleive that turning down a junior day shows that you are not interested. It was mentioned that it shows a lack of interest on the players part. That advice is not correct. You are sending the wrong message here. If you are a true prospect to them, you will remain a true prospect regardless of a junior day visit or not. And you ask your son to be responsible to call or email the coach with the truth (commitments, too far to travel, money, etc.)
Almost every school that invited him to junior day still called July 1 or that week.