I agree with Irish Lass. You need more firm fats and/or waxes to make a balm that has better staying power on the lips. A balm with a high % of liquid fats might glide on very nicely and feel great on the lips, but it won't remain on the skin as long and will melt easier in the pocket or on a hot day.
Cocoa butter is a good choice for lip balms because it has a higher melt temperature than many of the other butters. But it still melts just slightly above body temperature. You most likely need to raise the melt temperature of the balm to get the staying power you want.
Working with your recipe, I'd try increasing the amount of beeswax by maybe 5% and reduce the sweet almond oil (SAO) by that same %. Test and see if that works better. If it's still too soft, increase the beeswax by another 1-2% and reduce the SAO by the same amount. Test again. If too firm, reduce the beeswax and add more SAO.
Adding a bit of lanolin is another good tip from Irish Lass -- it is a good barrier for moisture loss and softens the skin nicely. It will also reduce the liquidy-ness of your balm without making the balm overly hard like beeswax can. A little lanolin goes a long ways though. I'd dial in your basic formulation first, and then do another trial with lanolin at Irish Lass's 10% and see what you think.
I use only liquid oils and beeswax in my lip balm, so my recipe needs proportionately more beeswax than Irish Lass does to compensate for not having any butters in the formula. Staying power in a lip balm is all about melt temperature. There are many perfectly fine ways to get the melt temperature to be correct for your needs. Here's my no-butter formula so you can compare it with with your and Irish Lass's recipes --
Sunflower 33.8%
Jojoba 33.8%
Beeswax 31.5%