Q. "At what point does independence become isolation?"
Well folks, that seems to me like a bit of a loaded question. With independence comes weight. Often times, when the load gets heavy people flee because they aren't willing to share the burden, however, on the other hand responsibility becomes pride and we all know what comes after pride....the fall.
After getting so accustomed to being independent, you find solace in alone time because while being so fiercely self-sufficient typically you inevitably become dependable so people come around to add to the load as opposed to share it because you can handle it all or so they perceive. That life can become isolated because that convenient and necessary alone time can become addictive due to the peace you find. The flip side of that is after getting hooked it's hard to get off and at that point what started out as just independence has become true isolation. You get fed up with being everything to not just yourself but to everyone who calls on you. You get tired, but honestly you have to question if it's all your fault. How do you get out of this tangled web? I suppose you forcibly burst your own bubble and start cutting away at the web.
Balance is important. Knowing limits makes a world of difference. Making conscientious decisions and not just going along with everyone's demands makes or breaks you.
If no one has shown you today, I love you but God loves you better.