I don't really know what I did here. I cut off the bottom little cross guy on the stem of the airlock because it was getting clogged up during vigorous fermentations. Now the middle piece just kind of sits on top of the stem and doesn't move at all, even though I know there's fermentation going on. I didn't have this problem until I cut the bottom pieces off of my airlocks. Please advise, as I've got 20 gallons in fermenters right now and am having this problem with 3 of the airlocks.
It just means that air is escaping elsewhere, like around the bucket lid in one, two, or a few places, or from around the grommet around the airlock. If you've had many vigorous fermentations using your buckets (and I'm assuming buckets here--this isn't likely to happen with a carboy unless your stopper is too small), then there is a good chance there are other leaks. Not a problem.
As long as your beer is actively fermenting all outside air is still being pushed out and away from your beer. This will expel and prevent entry from any nasties that could harm your brew.
Airlock activity is not a good gauge of how well your batch is fermenting, and wherever your small leaks are, they're not likely to allow any contaminants in, provided that you don't go for months without racking, of course.
PS--If you are using carboys, you should be using blow-off tubes instead of airlocks to deal with this sort of thing.
Cutting the little cross-hatches off of a three-piece airlock will do nothing to harm the basic operation of the airlock. They work on air pressure. It is likely one of three things: