Your tent stopped being waterproof. What now?
Short answer
Work out which of three things failed. Water soaking in rather than beading is worn DWR and takes a wash-in reproofer. A sticky, flaking, smelly fly is the polyurethane coating hydrolysing, and that is the end of the fly. Wet lines along stitching are the seam tape lifting, which is repairable.
Worn DWR
The finish that makes rain bead up wears off with use, dirt and UV. The fabric is still waterproof underneath; it just wets out, gets heavy, and feels like it is leaking because the inside is damp with the condensation it can no longer shed.
A wash-in or spray-on reproofer restores it for a few seasons, and it costs a fraction of a new fly. Clean the fly first — reproofer over dirt does not stick.
Hydrolysed polyurethane
A polyurethane-coated fly stored damp, or simply old, eventually goes sticky, flakes, and smells. This is the coating chemically breaking down and it cannot be reversed. Some people strip and re-coat with a silicone-based sealant; most replace the fly.
It is the specific reason silicone-impregnated fabrics are worth paying for on a tent you intend to own for ten years, and the specific reason every tent should be dried completely before it goes in a cupboard.
Failed seam tape
Water appearing in a line along stitching, rather than over an area, is tape lifting. Peel off what is loose and run a bead of seam sealer along the inside of the seam. It is an hour and about ten dollars.
Some shelters — particularly silnylon and silpoly ones from smaller makers — ship unsealed on purpose and expect you to do this once when the tent is new. That is worth knowing before the first wet night rather than during it.
Tents this comes up with
MSR
MSR Elixir
15.0 sq ft each
Six Moon Designs
Six Moon Designs Lunar Solo
26.3 sq ft each
Kodiak Canvas
Kodiak Canvas Flex-Bow Deluxe
16.7 sq ft each
More of the same kind of thing on tent specs, explained, or start from a filtered list.