Discrete PID/ Discrete integrator

Hello:

I have implemented two discrete PID in parallel. The input to the first one is always positive but the second changes its sign during the simulation time. The problem is that the second PID does not give any output. I have separated its components and seen that the problem is the discrete integrator. Is there any limitation for the input(very samll value, sample time, change of sign, ...)?

Thank you in advance