The phrase "indomitable spirit" means having an unyielding and unbeatable mindset or attitude. It describes someone who never gives up, even in difficult situations, and remains strong and determined. Full definition
Dawn, «Indomitable spirit of hope» — I can always count on you for recapping my thoughts in your own strong, smartly worded way (while also knitting in a compliment (thank you!). (careertrend.net)
He had fought for good health on and off for a number of years with the same indomitable spirit that led him to many a victory on the river both as oarsman and the architect, as Head Coach, of a record series of Boat Race victories for Oxford over rivals, Cambridge in the 70s and 80s. (sport.ox.ac.uk)
August recently made headlines because the ending may change from what audiences saw at TIFF, and that would be for the better — I somehow doubt that reassuring viewers of Julia Roberts's indomitable spirit ever crossed Letts's mind as one of his goals for the piece — but it wouldn't be enough to take the Garry Marshall tang out of the film. (filmfreakcentral.net)