Why would a man keep messaging me out of nowhere?

He’s 36, very handsome, settled, quite successful and currently single. We met each other on Bumble, and he stopped using Bumble after he got my contact info. He’s a bit older for my taste but very good looking and I am very attracted to him.

So, we talked daily and he wanted to come and visit my city to have a date. But I refused, I was recovering from a break up and wasn’t ready.

His communication got less frequent, but he still messages me once in 4-5 days and we talk whole days, he keeps saying he likes me.

But I don’t know what else does he want, he is not implying anything. Is he just messaging because he likes messaging? Why wouldn’t he try visiting me again? I don’t see the reason why should I keep messaging him.

Updates
+1 y
We don’t speak about anything sexual, we just flirt subtly and he keeps telling about his days and whereabouts.
Updates
+1 y
He’s doing that again. He just messaged me he’s invited to have lectures in the nearby city and he would like to have a date with me during or after the trip. He hasn’t messaged me for 3 weeks and just messages me that today.

I Just don’t understand why, he lives very far from me, he’s got his own business in another city, I live very far from him and what is he expecting from this date? I told him in the past, I am not into casual relationships, then why does he want to meet me? What will on?
Why would a man keep messaging me out of nowhere?
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