Guys, Should I give up on him?

Anonymous
I met this man some time ago, and felt like there was a “spark” when we were introduced, but we remained casual acquaintances for about a year. He then started pursuing me for sex out of the blue, and when I made it clear that I wanted to get to know him a bit better, he backed off. I boldly suggested hooking up after some time, but he turned me down flat, and things cooled off as I realised that I didn’t mean that much to him. He stayed in some sort of contact though. Several months later he reappeared with a “smoother” approach, calling me “special” and “beautiful”, and we started hanging out again. He contacts me from time to time, and our meetings are very sporadic, like once every 3 weeks or so. He used to kiss me hello and goodbye, and we made out heavily once, but that was as far as it went. Now we are in more frequent contact, but he has stopped initiating any kind of physical contact with me. The truth is that I want to initiate, but after being turned down last time, I am afraid to. I am very confused as to what he wants. He seems eager to meet me, and we have gotten a bit closer than mere acquaintances, but I am not sure if I have been friend-zoned or not… Last time we met, I invited him over for dinner, we had a great time but he didn’t so much as touch my arm. (by the way we are in our 40s.) Why would he stay in my life if I were only a casual hookup option? Could he be expecting me to do something this time, as he was the one doing most of the pursuing before? I feel that I was responsive to him though; it’s not as if I were acting cold and not giving anything back… Opinions welcome!
Guys, Should I give up on him?
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