i know danes have a tendency to get cancer and mastitis might be an early warning in them. but ...
we had a lot of OEM litters and while sometimes the mom got mastitis, they didn't get cancer. i remember my mom would always regularly check the nipples & watch for this problem. if the signs were there, she would automatically start warm compresses. and we never spayed them because of mastitis.
and just because they got it once, that doesn't mean they'd get it again. sometimes a new mom would not rotate her pups to all nipples and that could cause it. we had many who never had mastitis and several who had it only once. if this vet says she has a 50% chance of getting it again, i would ask what the chances are for a 1st time mom & for an experienced mom who hasn't gotten it yet.
in talking to my mom, we think you should get a 2nd opinion. Davis told us to neuter a puppy because he had 'severe hd'. he turned out to be a top show dog with great hips and no hd once he grew up. this was a long time ago and is only to demonstrate that the vets don't always know what's best. i'm glad your here asking what others have experienced with their BP. i think as a whole, we have encountered more issues than any one vet could dream of.
what would i do? definitely not spay her just because she has experienced mastitis. like you said, women experience it all the time but that doesn't mean having another baby will bring it on again.