Why is Diels–Alder adduct exo when we leave it for a while? Recently we did an experiment of Diels–Alder reaction and we left the adduct overnight. I've read a paper of Woodward that says the adduct of Diels–Alder thought to be endo, whereas in our experiment it turned out to be exo.
As you probably know, the Diels–Alder (DA) reaction is reversible — the easiest example is the reaction of cyclopentadiene, which polymerizes at room temperature, which — if needed as monomer — has to be cracked just in advance.

In terms of the selectivity you observed, the endo-oriented product of the DA reaction often is the kinetic one, the exo-oriented product the thermodynamic preferred one.  Which is, if the rate of a DA reaction is to be increased while still obtaining endo-preference, an increase of the reaction temperature is skipped in favour a Lewis-catalysis, addition of a perchlorate, or high (external) pressure.