It's incredibly common for greys (we have four) to have bald or patchy fur on their thighs/butt, so much so that some greyhound rescues have classes at their shows for Baldy Butts or Baldy Bottoms and in the US the rescues call it a Shiny Hiney!
For non greys this can sometimes be an indicator for thyroid problems, but for greys it is absolutely normal, and I would only be worried if there were signs of itching, redness etc. in which case vet, pronto.
you will often find that once they have been through a moult cycle in your home and got used to the lovely soft armchairs and beds, that you do get some regrowth. Unfortunately this often looks like a teenage boy trying to grow a beard for the first time - rather pathetic wisps of fur with comedy bald bits in between.
Is she a rescue greyhound? Ours is and a few weeks after we adopted him (Jan 2010) his fur started coming off in chunks around his thighs/backside. I was worried sick I had done something wrong. We emailed photos to the kennels where we got him from. Apparently, since they are used to a less than idyllic outdoor life this is their reaction to a nice home with central heating in the winter. They malt in excess. It only happened in this extreme way during the first winter, after that he has settled firmly in and, while he malts a little every winter, he is not the bald backside boy that we had during the first year.
I agree that you should seek advice if you are still worried and if she is licking excessively for example.
I am not a greyhound owner so I don't know if this is specific to breed, but I would personally take a dog to the vet with unexplained hairloss. Things like fleas or mange can causes baldness if untreated
For some unknown reason, NiceDog (5yo greyhound), is rapidly losing all the hair on the back of her thighs - she'll have a bald backside soon at this rate! Her skin looks fine, no signs of infection or irritation; nothing stressy has happened (Xmas was nice and calm); there have been no changes to her diet, and it's not caused by rubbing off on her coat or the way she sits/lies. We've had her for 6 months and her coat has been lovely until now, so it's puzzling me like mad why this is happening (although it doesn't bother her one bit!). I know it's not uncommon for some breeds to have bald bits, but any ideas on how to encourage her hair to regrow - any natural supplements or lotions I could use?