So

Theory: the ml might just 'give up', but by then he may have already made an impression on the mc to get her a bit more conscious of his sudden disappearance; I think this awareness is the gap/chance that the ml wanted to receive

Your typical Hot-and-Cold tactic! Well- at least that's how many shoujos/romance stories would go. If the author decides to add twists and divert from this (kinda) cliche, then I'll be very happy :3 but yea, for now, that's one way it could go