We consider 1+1 Yukawa model in the strong background field (namely, linearly growing scalar field). We derive exact harmonics, calculate the fermionic current and find that it grows logarithmically. We reproduce this result by integrating out the fermion degrees of freedom in the effective action. Finally, we calculate loop corrections to the scalar and fermion propagators and observe that they receive growing with time infrared contributions. This indicates the breakdown of the perturbation theory.