In Robinson Crusoe, once you build the brick, what happens to it?
As I understand it, the brick increases the palisade level by 1 when it is built. Then what?

It is placed in the invention spaces.
Rules, p. 18:

At the end of the Action Phase, any Inventions in the Future Resources space will
trigger their effect, be flipped to the Item side and then placed in the Invention
spaces on the board (even personal Inventions).

It is not turned over to be built again on its own, but if some effect turns it over, then it

undoes its effect (you lose 1 palisade level)
Can be built again.

Rules, p. 18:

The Brick increases the Palisade level by 1. If, later in the game, it is flipped
to the Invention side, the Palisade level must be reduced by 1. If this is not
possible, nothing happens.

Rules, p. 18:

During the game, an effect may force players to flip Items back to their Invention
side. From the start of the following round, such an Item ceases to be available
(it is still available for the current round). It must be built again before it can be
used.