Fair enough - but you'd reckon a minister of religion would at the very least believe in God!
Yes, but it's possible to lose one's faith. And the stats given here indicate that only 3% of the ministers doubt the existence of God, as compared to 10% of the general population (at least in America). The reluctance of these priests to resign can be explained by the fact that there aren't many employment opportunites outside the church for former priests that don't involve heavy lifting.
The number of doubting clergy also roughly corresponds to the percentage of priestly homosexual ephebophiles (2%).