Vent pipes, if installed correctly always should have a pitch to allow condensation to flow down into the sewer system.
I had a vent pipe leaking in my attic. I thought it was a roof issue and that the pipe wasn't sealed properly. What actually happened is that the vent stack got pushed down to where any condensation was trapped in the pipe rather than flow back down. No problems in the summer, but in the winter the pipe would freeze because it was full of water. As it thawed it dripped and one of the tee's was not sealed properly so it leaked there.
I am not sure if this is your issue but I bring it up for your consideration.
It's unfortunate that vent pipe isn't always given the same attention as drain pipes when assembling. Many assume it will never have to carry any water so they slap it together and forget about it.