We investigate the stability of a composite cyclone representative of Arabian Sea eddies using a high resolution primitive equation model. We observe that the eddy is unstable with respect to a mixed barotropic/baroclinic instability, leading to the growth of an azimuthal mode 2 perturbation. The latter deforms the eddy, which eventually evolves into a tripole after about 4 months of simulation. The presence of a critical level for the most unstable mode generates sharp fronts in the surface mixed layer where the Rossby number is large. These fronts then become unstable, and this generates submesoscale cyclones and filaments. Near these fronts, diapycnal mixing occurs, causing the potential vorticity to change sign locally, and symmetric instability to develop in the core of the cyclonic eddy. Despite the instabilities, the eddy is not destroyed and remains a large-scale coherent structure for the last 6 months of the simulation. Looking at Sea Surface Height only, the composite eddy evolves little, and fairly represents the eddy observed in the altimetry which can live for several months. The study of this simulation thus illustrates the numerous kinds of instabilities which may occur in large cyclonic eddies but can not be captured directly by altimetric data.