We present an asymptotic Padé-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass m_A = 100 GeV, into two gluons. All but one of these coefficients are shown to be determined for arbitrary m_A from the known three-loop-order rate by renormalization group methods. Asymptotic Padé-approximant estimates for these coefficients are all seen to be within 12% of their correct values. The four-loop term in the decay rate for m_A = 100 GeV is estimated to be only 4.3% of its leading one-loop contribution.