  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.
