It sounds as if your bird's wings are not clipped. I would take
her to a reputable AVIAN vet and have her wings clipped - make
sure it's an african grey clip. They can't be clipped as short
because they are heavy bodied birds and will crash and split open
their breast with their keel bone if they are clipped too short.
They can only have 4 or 5 primaries cut up to the level of the
first coverts. Your vet should know what I'm talking about.
I think you are not being patient enough. All birds go through
different stages where they don't want to be held, then do want to
be held, and on and on, depending on their mood or the time of
year. Hormones don't last all year. This is mating season for
greys so all people are having a bit of trouble now. It lasts a
couple of months. There are many things you can do but I can't
outline it all here. If you have not read Guide to a Well Behaved
Parrot by Mattie Sue Ethan, I suggest you get it now and read it
all, especially the part about behavior. You need to do even more
research about african greys in particular and Bird Talk Magazine,
found at most pet stores, has an article every other month about
african greys and I know if you wrote them, they have many back
issues about them that you could order directly from the magazine.
You really also have to accept the fact that sometimes birds just
don't want to be stroked or held, just like sometimes you don't
feel like having someone in your face or putting your arm around
you, or whatever. You have to give the birds some choice in the
matter. If the bird is in the mood to be touched, you have to go
slowly, perhaps petting their head with one finger, or along their
spine. As time goes by, you can try expanding petting to other
parts of their body. I have one bird who likes his head and
cheeks petted but another bird allows her back and head to be
petted, and under her wings. This didn't happen overnight. You
have to gain the bird's love and confidence and go gradually.
Even so, there are times when they just don't want to be petted.
It has to be on their schedule, not mine. I would not keep
getting a different bird and starting over again; even a male has
hormonal periods where they're more likely to be ornery. You have
to work with what you've got and take your time and give your bird
a chance to get used to being touched. The wing clipping will
make the bird more dependent on you and it won't fly away when you
go to get it. You can also offer a treat and praise for when it
comes back to you. Good luck and keep us posted about your progress.