To my knowledge we've never had a major (or even a minor) republican rebellion, the early political parties were republican and during the early 20th century they had the chance to peacefully abolish the monarchy but they decided to postpone it until the people had a chance to make their voices heard and I think it just stopped being an issue because the transition from a monarchy to representative democracy was pretty smooth and peaceful. We generally like our royals even if they are French newcomers.