Basically, the material is starting to break down. Firstly, they aren't that well made, which is why they are so much cheaper to begin with. Secondly, think about phthalates; you know that death-like smell that jelly toys have when you first get them? And they slowly start to smell a little less evil? That is the phthalates leaching out of the toys (into the air, into your body, etc). As they disappear, the toy's stability starts to break down, get sticky, etc.
I too recommend silicone; at the very least, TPR silicone. It's not that much more, and it's much better for your body, and will last longer!