Small flies keep coming back a week after every treatment — how do you actually end a fungus gnat problem rather than dent it?

You are killing adults, and adults are not the problem. That is the whole thing, and it explains the exact one-week rhythm you are describing.

The flies you can see live a few days and are almost irrelevant. What matters is in the top couple of centimetres of soil: eggs, then larvae feeding on damp organic matter and fine roots. Kill every adult in the room and the next generation emerges from the compost on schedule. Your treatments are working perfectly and hitting the wrong life stage.

So the target is the top layer of soil staying damp. Fungus gnats need moist surface organic matter to lay in, and they cannot complete the cycle without it.

What actually breaks it:

Let the top two to three centimetres dry properly between waterings. Not the pot — just the surface layer. Most plants tolerate this even when they want moisture lower down, which covers your two thirsty ones.

Water from the bottom for a few weeks. The roots get what they need and the surface stays dry, which is exactly the split you want.

Cover the surface with a centimetre or two of coarse grit, sand or bark. It is a physical barrier for something that has to land and lay in soft damp material, and it works while you are still watering normally.

Do those and the population collapses in one generation because nothing new is being produced.

If you want something that goes after the larvae directly rather than only starving them out, the standard one is a bacterial larvicide — the strain sold for gnats and mosquito control, in the form of granules you sprinkle or a product you soak into the water.

What matters about it, and what people get wrong:

It kills larvae, not adults. You will still see flies for a week or two after it starts working, and that is the point at which people decide it failed and buy something else.

It has to be repeated on the cycle, not once. The eggs already laid will hatch, and it does nothing to eggs. Applying it on the schedule the packet gives, for the full course, is what makes the difference — one application knocks the number down and the survivors rebuild.

Every pot in the room, at the same time. This is the other half of your reset. If you treat six of nine, the untreated three are a reservoir and the room repopulates from them. Treat all of them, including the ones with no visible problem, and including anything that came in recently.

Combined with the surface drying above, that is a real end rather than a dent.