Are you in her sight the whole time you are outside, or can she
go somewhere you can't see her? Does she go potty in the house in front of you or does she sneek into another room? If you are and she does then could be she was being smacked for going potty in the previous owners house and now is afraid to go when you are watching. She may think she was hit for what she was doing, not where.

I had a beagle 13 years ago and he was fully housetrained until I had a baby. Unfortunately, I was so wrapped up in my son's life and wore out otherwise that my dog was getting ignored. To get attention (even negative attention) he started using the house as a potty. Took alot of patience and time before he forgave me.