Frankly, if you found that your contacts will be folding when you are putting them in, I think you have done some wrong ways to put in them. As far as I know, there are two kinds of reason causing the lenses folded. On one hand, you maybe put so many saline solutions on them while putting them in, because the weight of the solution will make the contacts fold in half way. If so, it's OK, you just need reduce the solution then you can put in them softly. On the other hand, after putting them in, you should avoid blinking because if you blink too much, the lenses don't stick completely to your eyes causing some air bubbles between the lenses and your eye ball. If the folding is caused by it, you can just try not to blink and keep your eye open and look around in all directions to help it attach to your eye better.
Well, as a matter of fact, there are some reasons that can explain your problem. Well, the first reason is that you have been wearing the contact lenses for much too long each time, in this way, your eyes will feel extremely uncomfortable you know? So, I recommend you reduce the time. The second reason is that your eyes are much too dry, because it is the water that makes the lenses naturally staying in our eyes. So, I suggest that you try not to get dry eyes. Just give your eyes enough time to rest, and it will be ok.
You must soap your contact lenses in the solution during the time you don't use it. It will not be folded in this way. If the contact lenses are folded in your eyes, you'd better take them out from your eyes. And rewear them again. Or else, your eyes may feel painful and discomfortable.