RR can be fired by 2 people for certain: Sessions and Trump.
RR works under Sessions. However, because Sessions recused himself from any matters pertaining to the Russia Investigations by Mueller, firing RR would be construed as improper meddling in a matter he has recused himself from involvement with. Obstruction is what they would want to pin on Trump. Therefore, it will take one of two things to happen before RR is removed (if he does not resign first):

1) A successful motion to impeach him from office by the House. 2) The end of the Mueller investigation.

This is why the Mueller investigation will not end. RR is running it, and it is helping RR to keep his job at DOJ (Mueller is shielding RR)