We study the Kondo lattice model with the Heisenberg-type RKKY exchange coupling among localized f spins in the presence of a magnetic field. By means of an extended dynamical mean field theory combined with the noncrossing approximation, we investigate the one-particle spectral function and the dynamical spin correlation function in the Kondo insulating phase. It is shown that the magnetic field and the RKKY exchange interaction both cause instability to the antiferromagnetic order with enhanced transverse spin fluctuations, which give rise to a strong renormalization of quasi-particles as the system approaches the quantum critical point. This leads to a tendency to retain the Kondo insulating gap up to rather large fields.