A few thoughts:
If a friend of mine doesn't reply to messages that have no specific 'call to action', I assume they're busy or can't prioritise a response for whatever reason, not that I've done something to offend them, or that they don't value my friendship, or that they're 'blanking' me.
If someone says to me 'let me know if you fancy meeting up,' that doesn't feel like it necessitates a prompt response.
Whereas, if a friend says 'I'm in your neighbourhood next week, do you have time for a drink on Tuesday?' I'll reply right away so that they can plan.
And if they say, 'Let's plan a night out! When's everyone available?' I'll answer with my availability.
But vague 'how are you?' messages with a mention of possibly meeting up at some point, but no concrete suggestions or plans or dates that might work don't signal to me that I need to reply swiftly, particularly when I'm very busy or preoccupied. And after that it's easy for the message to fall off my radar.
If you really like this person (which I can't tell from your posts) it might be as simple as being more specific and assertive in your messages. If you want to meet up, suggest a time and place.
If the lack of consistent communication really annoys you or hurts your feelings, you're probably not compatible.
I've not found myself to be very compatible with people who find it anxiety-provoking or hurtful not to have a prompt response - however much we may like each other.
It feels like I'm always in the doghouse, and I get tired of feeling like that, as I'm sure they get tired of feeling like I'm blanking them or disrespecting them or whatever. Neither of us is right or wrong, we're just not compatible.