I don't think it effects your chances of getting another one.
I turned down a house through the affordable house new initive back in May this year.
I've since been offered an apartment from affordable housing.
It's though Meath County Council. After I turned the first one down (because I couldn't get as much as the house was as a mortgage) they then sent out a letter to get me to get a loan in principle letter from the EBS, so they knew how much I could get.