The lipid membranes of living cells are composed of a large number of lipid types and can undergo phase separation with the formation of nanometer-scale liquid-ordered lipid domains, also called rafts. Raft coalescence, i.e., the fusion of lipid domains, is involved in important cell processes, such as signaling and trafficking. In this work, within the framework of the theory of elasticity of lipid membranes, we explore how amphipathic peptides adsorbed on lipid membranes may affect the domain-domain fusion processes. We show that the elastic deformations of lipid membranes drive amphipathic peptides to the boundary of lipid domains, which leads to an increase in the average energy barrier of the domain-domain fusion, even if the surface concentration of amphipathic peptides is low and the domain boundaries are only partially occupied by the peptides. This inhibition of the fusion of lipid domains may lead to negative side effects of using amphipathic peptides as antimicrobial agents.