'X-Factor' Contestant -- Pressing On After Father Dies

42-year-old "X-Factor" contestant and single mom Stacy Francis was rocked to the core two weeks ago -- after learning her father had died -- but after an agonizing inner struggle, she's decided to continue with the show.

Stacy made it to round two last month -- receiving unanimous approval from the judges for her blowout audition (below) -- but soon after launching into the "X-Factor" boot camp, she received news her father had unexpectedly passed.

Sources close to Stacy tell TMZ -- Stacy strongly considered quitting the show to be with her family -- but ultimately decided to stay ... believing that's what her father would have wanted.

One source tells us, “it has been such an emotional roller coaster for her.”