Why does supermarket basil always collapse within two weeks?

Because it is not one plant. A supermarket pot typically contains twenty to forty seedlings sown densely together, grown fast under glass for a few weeks and sold as a short-life product. They are competing for the same small volume of root space and were never intended to live past the point of sale.

That crowding causes the classic failure: the outer plants dry out while the crowded centre stays wet, and stem rot works outward from the middle. Adding more water accelerates it.

To keep one alive, split it. Tip the whole thing out, soak the root ball in tepid water for ten minutes, and tease it into three or four clumps of five or six seedlings each. Pot each clump into its own container of ordinary compost, water in, and keep them somewhere bright and warm — basil wants real warmth and sulks below about fifteen degrees. Expect a week of wilting while roots recover.

Then change how you harvest. Cutting individual leaves off the outside leaves a bare stem. Instead cut whole stems back to just above a pair of leaves; the plant branches from that point and produces more than it had before. Never take more than a third at once.

Pinch out flower buds as soon as they appear. Once basil flowers it shifts resources to seed, the leaves go bitter and thin, and the plant declines regardless of care.

Honestly, though: a supermarket pot is cheap and disposable by design. If you want basil through a season, sow seed in spring — it germinates in under a week and a single sowing produces far more than any bought pot.