Why does my man not answer my calls for prolonged periods of time and disappear for hours?

I've been dating this man who is 17 years older than I and I am 45 so he is "up there" in age. However, he looks 10 years younger than his actual age and is very fit and quite attractive. We have been seriously dating for 4 months now and he is recently divorced. He keeps mentioning marriage to me and says he loves me very much but he frequently disappears for several hours at a time or even a day or two without returning my calls and sometimes shuts his phone off all together. I have talked to him to let him know that it bothers me when he just "disappears" without any explanation or a very strange story the next day. My gut keeps firing off that something is wrong but he always tells me he's not doing anything wrong. He often teases me too by saying, "How do you know I'm not playing you?" Which I find odd but I just act like it's a joke. Should I be suspicious? What should I do?
Why does my man not answer my calls for prolonged periods of time and disappear for hours?
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