Using the bounded-confidence model, with fixed uncertainties and extremists, we investigate how resilient the moderate mean opinion of a population is to the arrival in it of a new group of agents, when the energy of the opinion of this group extremeness x group size) is varied. We say moderate mean opinion is resilient when, even though it may become temporarily more extreme after the arrival of the new agents, it later recovers its moderate value. We show that such resilience is displayed up to a threshold value of the equivalent energy of the group. We also show that when the agent-based model spontaneously converges to a single extreme, then this energy threshold is nill.