The gasket seals by springing back, not by being crushed
A silicone gasket works by elastic deformation: it is squeezed, it pushes back, and that push fills the gap between lid and rim. There is an optimum amount of squeeze. Past it, more torque buys nothing — the seal has already reached its pressure — and the material starts to take a permanent set. Leave it compressed hard and long enough and the gasket stops returning to its round section; it stays flattened, and a flat gasket pushes back with less force than a round one.
That is the trap. The gasket flattens, contact pressure drops, it weeps, and the natural response is to turn the lid harder — which flattens it further. It is a loop that accelerates itself, and it ends with a gasket that is a hard, flat ring with a crease in it. The repair is not more force, it is a new gasket and a change of habit: turn until it is snug and stop. Most lids have a mark, or a point where the resistance rises sharply, and that is the end of the turn.
Three places, three different answers
Between lid and rim, with a gasket that still feels round and springy, is a seating problem: the lid went on cross-threaded, there is a crumb or a dried film in the thread, or the rim is not flat. Free to fix, and free to diagnose with the paper test: lay a thin sheet of paper across the rim, screw the lid down, then try to draw the paper out. Where it slides easily, the seal is not contacting — that side is low, or the lid is not square. Where it grips all the way round, the sealing face is fine and the leak is coming past the thread or through a vent.
The gasket itself is a material problem, and the test is your fingers: take it out and squeeze it. Round, springy, returns instantly — it is fine. Hard, slow to return, or leaving a flat spot where you pressed — it is done. When you buy one, match the section shape as well as the diameter: a square-section gasket replaced with an O-ring turns a broad contact face into a single line, and it will leak at the same pressure it used to hold.
Under the base is not a gasket problem at all. A vacuum flask is two stainless walls with a vacuum between them. If water appears underneath, the inner wall has a crack and water is getting into that gap; if the outside gets hot with hot water inside, the vacuum is gone. Either way the flask has lost the thing it was bought for, and no gasket will bring it back.