I-ball/oscillon is a soliton-like oscillating configuration of a real scalar field which lasts for a long time. I-ball/oscillon is a minimum energy state for a given adiabatic invariant, and its approximate conservation guarantees the longevity. In this paper, we examine the stability of a special type of I-ball/oscillon, the exact I-ball/oscillon, whose adiabatic invariant is exactly conserved. We show that the exact I-ball/oscillon is stable in classical field theory, but not stable against small perturbations depending on the value of its adiabatic invariant. Accordingly, the exact I-ball/oscillon breaks up in the presence of the fluctuations with corresponding instability modes. We also confirm the fragileness of the exact I-ball/oscillon by the classical lattice simulation.
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