You might be rolling it too thin... thats the only time I've experienced tears, but it's definately because it's too thin (for me anyway). I roll to a little less than an 1/8". Not quite to 1/16". I've found that 1/16" is too hard for me to work with.
Do not let it sit before you drape it on the cake. Fondant dries very quickly. It's hard to say why it is tearing without more details, but it could be that you have rolled it too thin or that it has dried out in spots because it wasn't placed onto the cake quickly enough.
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