The Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation, governing the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform magnetic field in a non-thermal plasma, admits soliton solutions having a sech2 profile. The higher-order growth rates of instability are obtained using the method developed by Allen and Rowlands [J. Plasma Phys. 50, 413 (1993); 53, 63 (1995)]. The growth rate of instability is obtained correct to order k2, where k is the wavenumber of a long-wavelength plane-wave perturbation. The case where the coefficient of the nonlinear term in the KdV-ZK equation vanishes is also considered.