The white growth is not an issue, as Kevinsky says - you've added a picture of the outer pot it was standing in all this time; because the outer pot was close fitting, and water would have been sitting in it, roots have come out of the bottom and sat inside, wet or damp, and this white growth has formed. My advice is going to be very similar to that given in two of the other answers.
The reason your plant 'sometimes gets sick' is because it needs a new, bigger pot. Use a pot with drainage holes a size or two larger, and new potting soil, decant from the existing pot (it doesn't matter if you break the roots hanging out of the current pot) and repot, water in well. Allow the pot to drain down thoroughly, then place it back in a tray or outer pot.
When a plant has filled its current pot with roots, the ratio of soil to root is wrong, so it can be difficult for the plant to take up sufficient water because there's not enough potting soil to hold it for long. In this case, the roots have grown outside the pot because that's where water could be found. Ongoing, when you water, water thoroughly when the surface of the soil feels just about dry to the touch, then empty out the pot or tray it's standing in after 30 minutes so it's not left sitting in water.