For whatever reason when I try to mask my tanks with masking tape, the paint somehow gets beneath the tape and sort of also builds up around the edges. I'm at a loss as to why this happens. Is there something specific I'm doing wrong?

The reason it builds up is that you either apply too many cotes or the tape is too thick. Tamiya tape or Frog tape work well. I personally use blue painter's tape. You should burnish the edges of the tape, before painting. This should keep the paint from getting under it. What type of paint:thinner ratio are you using and what type of paint?

Tamiya acrylics about 50/50.

Sounds like you are getting paint - pooling along your tape-edge, and as long as that paint is as thinned as you have it, there's plenty of chance for pooled paint to slip under the tape. Aside from snugging that tape (burnishing) as Matt suggested), you probably should spray your coats lightly and let dry some between passes to avoid pooling.

Bob

Burnishing the tape will definitely help. I almost always use a piece of wood to rub down the edges of the tape. Popsicle sticks work well;rounded toothpicks are great for tight spots.
If you like to buy tools, go to an art supply store and get wooden sculpting tools for clay. The work great.

Jordan,
As other suggested light passes of the airbrush...don't flood
the area.

Also this will help a lot.....always spray in the opposition
direction to the tape's edge and not towards it...adjust your
airbrush angle accordingly.

Cheers,
Joe

+1 on what Bob said, and Joe's advice on the direction of spraying is good, too.

Previous suggestions are all good, but here's a very good trick to keep paint from creeping under your mask:

Mask as usual. Burnish however you want - it doesn't really matter with this method. Before spraying your next color, spray with clear first. Anything that creeps under your mask is clear, so it doesn't matter. Now shoot your next color. Guaranteed crisp lines every time.

I spray the clear first as Rob says. Works great every time.