I have found a Shock Glaive+1 and I m wondering if I am still able to re-roll the check after I already discarded the weapon to have the bonus dice, in case I fail the check (in other words if I can re-roll discarding the weapon that is already discarded in the same check)?

Has anyone experienced that?

Nope, you can't discard an already discarded card. So most of the time you will not be discarding the extra d8 unless you are in a really tight spot.

Ok, thanks mate