when booleaning and doing those unions, you just have to make sure the two polygons go into each other with a good amount of distance. meaning two polygons should go into each other quite a lot to not have them dissapear when you use the boolean tools.
you probably can't boolean two objects that almost barely are touching each other.
so if you just push or force your two polygons closer into each other, you should be able to do a boolean, if not, your polygon models are modeled too complex or (your edges and vertices don't flow in an organize matter) for maya to be able to calculate and boolean them.
hope that helps.
9 months into Maya...and still learning...
0 experience with any other 3D programs