From my research there aren't really any lip balms that last 24 hours even though some might say so. Realistically reapplication every 3rd hour or so is the best I've seen under dry conditions.
This is a personal issue of mine, I have dry lips in winter (low humidity) and I don't want to reapply lip balm every 2 hours.
It seems like waxes alone wouldn't do the trick, you'd need an occlusive that adhered to the lips a bit like glue to stay on through meals etc. Maybe there are some silicone waxes that could get you part of the way there combined with some glue like substance (what do they use in peel off masks?).
Another or complimentary approach would be to use some sort of long lasting humectant or other kind of moisturizing agent (e.g. urea), but I don't know of any that would be potent enough on their own.
I think it's fairly obvious that this product would sacrifice some sensory performance for longevity, but it could be a great niche product for people like myself, mountaineers (with SPF added) etc that don't enjoy the lip balm experience.
Can we crowdsource a formula here? I've never formulated a lip balm so I'm afraid I don't know where I'd start.