http://www.federalreserve.gov/aboutthefed/section%2010.htm
...each member shall hold office for a term of fourteen years from the expiration of the term of his predecessor, unless sooner removed for cause by the President. Of the persons thus appointed, 1 shall be designated by the President, by and with the advice and consent of the Senate, to serve as Chairman of the Board for a term of 4 years...
Which means she can be impeached.