Rovers were booed off by their fans at full-time following defeat by the Robins, in what was their fifth consecutive home league loss.
They have the scored just three goals and conceded 27 during their losing run – which stretches back to the first weekend of October – and possess the worst goal difference in the division of -23.
Clarke, 47, was appointed in place of Inigo Calderon in May.
And, after losing the first three league games of the season, he seemed to have worked similar magic to his first spell in charge with a run of five wins and two draws that led them towards the play-off places.
That proved to be a false dawn in October, when a narrow defeat at leaders Walsall, where they led at half-time, began their unwanted run of defeats, including 4-0 hammerings by Milton Keynes Dons, at home, and Crawley Town and Barnet away.