Either/or. You can have tiny tiny tiny hairline cracks. Or the pot/saucer material could just be degrading. Or the material could be cheaply made.

In the end, don't put bare clay/ceramic or even glazed material on anything you value like carpet or nice wood on a desk/shelf. Inevitably, the water/moisture/condensation will get through and stain/damage. It's a losing battle, no matter how careful you try to be. I know you might find it ugly, but use a plastic or composite saucer underneath. Or move the plant onto tile/flooring/shelving/a surface that you don't care if it gets stained or damp. And using a ceramic/clay saucer under a ceramic/clay pot brings you back to square one of the problem.

Of bigger concern, in my humble opinion, is why isn't water "spilling" through the drainage holes? You need to be watering so at least some water flushes out each and every time. This is where the saucers come back into play.

Rule #1 for Amateur Container Gardening 101 is never ever ever install your container plants into a container/pot that doesn't have drainage holes. Either drill holes in the bottom or find a better pot with holes. Just like heart disease is the leading killer of humans, lack of drainage holes is the leading killer of potted plants through the ages. :)