I hear this line a lot. For all the talk of strong self esteem and independence our culture is fixated on, there really are a lot of fragile egos out there. One of the popular gimmicks I see out there is the 'frame a positive as a negative in a shallow attempt to appear introspective.'
Here, she basically tells us that she is consistently rejected by men because of good things. She is 'very attractive' and independent, but for some reason, these positive traits alienate (or 'intimidate') men.
It's far more likely that she is being consistently rejected on substantive reasons: she doesn't have the qualities men in her life care for. All that means is she has to get new men in her life, that's all. If they all reject her, it's more likely than not that she is being rejected for legitimate reasons (she is an unappealing companion) than for shallow ones, or being rejected for her strengths (good looks, independence, etc.).
She doesn't have what men in her life are buying. If she was genuinely intelligent, she would adjust. Instead, circumstantial evidence suggests she hasn't adjusted her approach as she reaches her 38th year. If something doesn't work, don't stick with it! Change! She either hasn't changed meaningfully or has changed in a poor direction.
Odds are people tend to be rejected for substantive reasons, not for their supposed strengths or good qualities. Sometimes people go to great lengths to believe a self serving 'limitation' rather than clearly evaluate things and actually change.
If the woman in the letter is for real, she will keep having the same problem until she adjusts. The adjustments may just be minor, but she has to make them to make positive change.
Its rare to find a man who really wants a truly independent woman. That kind of a man has to equally if not more strong in character.
They're becoming a rare breed in today's society.