Undoubtably, swimming farther without stopping requires dedication and breaking through mental hurdles. However whenever I watch swimmers (including myself about 8 years ago) who have to stop every lap or two, it's clear that they're flat out winded. Even if they're in good cardio shape. If they're not, the process of learning (say 3-months of trying to improve) will inherently build their cardio capacity.
They key is to burn less energy
while swimming. I'll make up some numbers: it seems like beginning swimmers use 80% of their muscles, constantly firing. It looks like thrashing or horizontal hip-hop. Conversely, it seems like good distance swimmers are using about 30% of their muscles.
Anyway, it is totally normal. I'll second Coach Stuart - learn the techniques of balance in the water (get those feet up w/o kicking), streamlining. Gotta relax. That'll get you there. Some keys to my learning were Terry's talks: