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I-ball/oscillon is a soliton-like oscillating configuration of a real scalarfield which lasts for a long time. I-ball/oscillon is a minimum energy statefor a given adiabatic invariant, and its approximate conservation guaranteesthe longevity. In this paper, we examine the stability of a special type ofI-ball/oscillon, the "exact" I-ball/oscillon, whose adiabatic invariant isexactly conserved. We show that the exact I-ball/oscillon is stable inclassical field theory, but not stable against small perturbations depending onthe value of its adiabatic invariant. Accordingly, the exact I-ball/oscillonbreaks up in the presence of the fluctuations with corresponding instabilitymodes. We also confirm the fragileness of the exact I-ball/oscillon by theclassical lattice simulation.

Fragileness of Exact I-ball/Oscillon