LOL!  Sorry I don't really have any suggestion other than she might not realize she's doing it.

Does she do it to women, too?  In some cultures, when a woman looks a man directly in the eye it means (to them) that she's interested and/or available.

i used to have this problem, like a kind of social phobia i was terribly shy, i still have problems talking to strangers and looking directly into their faces and i cant understand why i am like this. I am also a nurse, so part of my job is assessing people and talking to consultants, patients, doctors etc but its like ive developed a different persona when in nurse role, I think my job though has done a lot for my socializing skills and self confidence.

Its an awful predicament to be in and it makes it very difficult to make friends, i used to think people just spoke to me out of politeness maybe this was why i found it uncomfortable to look into their eyes, its a nervous/lack of self confidence thing which i think is responsible-this lady is probably crying out for a good friend but probably feels self conscientious.

There are also forms of autism which causes this too.