There are two issues in soap longevity -- hardness and solubility.
Hardness is a physical characteristic -- is the soap hard like brick or soft like clay? Hard soap will not abrade away on the washcloth as fast as a softer soap. Although most people think a hard soap is a long lasting soap, that will be true only if the soap is not overly soluble in water as well.
Solubility is a chemical thing -- how fast does the soap absorb water and/or dissolve in water? A more soluble soap will disappear quicker in water and a less soluble soap will not. An indicator of solubility is how quickly the soap soaks up water if left sitting in a wet soap dish. Low water solubility sounds like a good thing for a long lasting soap, but it has to be coupled with reasonable hardness as well.
A soap made with "brittle" fats -- coconut oil or palm kernel oil -- will be relatively hard ... but it will also be very soluble. The traditional "cold water" or "hard water" or marine (salt water) soap is a coconut or palm kernel soap known for it's abundant lather.
A soap made with soft liquid oils -- monounsaturated oils (olive, almond) or polyunsaturated oils (safflower, sunflower, corn, etc.) -- will not typically be a hard soap, but it will be a less soluble soap. As the water temperature goes up, however, so does solubility, so soaps made with some unsaturated fats will lather better and clean better in warm to hot water.
The base oil in a typical soap recipe should be the firm solid fats -- palm, lard, tallow, etc. -- with high levels of palmitic and stearic fatty acids. Soap made from these oils are abrasion resistant and not overly soluble. This type of soap can be mild, hard, and long lasting, but the lather can be minimal especially in hard or cold water.
So how to make a long lasting soap that is nice to use? Lots of ways, obviously, as all the discussion on this forum shows.
But one approach is to choose a firm solid fat as the base oil in the recipe to add firmness and longevity. Include some brittle fat to increase the lather, get better performance in cold or hard water, and add to the physical hardness. Add liquid oil to add some mildness and good performance when used in warm to hot water.
And finally look at additives that can add to the properties you want to enhance -- sodium lactate for hardness, sugar for more lather, a chelator (citrate or EDTA) to reduce soap scum, etc.