I have never done zero inflated Poisson regression but I have seen this in logistic regression when there is a perfect boundary between the two outcomes. Below I show a toy example that produces the error. I also plotted the data to show the boundary. Since you are fitting to two variables, you may be able to plot the data in a similar way and look for a boundary. Since you are fitting a Possion, I assume you have at least a few levels of counts, so a plot may be less useful.
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 3.5.3
DF <- expand.grid(1:10, 1:10)
DF$Y <- ifelse(DF$Var1 <= DF$Var2, 1, 0)
model <- glm(Y ~ Var1 + Var2, family=binomial(link='logit'),data=DF)
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
ggplot(DF, aes(x = Var1, y = Var2, color = factor(Y))) + geom_point()

Created on 2019-10-27 by the reprex package (v0.3.0.9000)