The problem is the air vent, but there is no easy way to get the bottle off once the vacuum is created. Drilling a hole on top will release the vacuum, but you'd better be ready to start draining into other containers. This is best done outside, if possible, because there will be spillage. Once you get the bottle off, pop the plastic funnel out (some require you to turn then pop) and clean the air release valve.
We have the same issue. I thought I could help equalize pressure by drilling a 1/8" hole at the highest point of the (inverted) bottle. Water immediately overflowed the reservoir. Weird thing is, not every bottle does it (even though they're all the same brand/size bottle).