I have had my Betta almost two and a half months and have only seen him swim through his cave one time!
I realize he has probably swam through it more than this, but I watch him often and have only witnessed it once. He has a Betta log and swims through it often, but just ignores his cave.
He is very active and swims through the plants in his tank constantly, weaving among the stems and leaves, tunneling through the massive overgrowth of java moss (that again needs to be trimmed as it's taking over the whole tank), but his greatest delight comes from wiggling through the floating moneywort and anacharis. Could it be that since he enjoys swimming through and peeking out from his plants so much that he doesn't need the cave in his tank?
I would really like to remove it (and add more plants in its place) if it isn't actually necessary to provide a cave for them to hide out in.
So what do you think? Are his plants and Betta log enough to provide him hiding spots? Do some Bettas just simply not care for caves?