Luckily there is a really quick and easy way of avoiding this. Simply pop your eye pencil in the freezer 10-15 minutes before using it. The cold conditions will harden the pencil, making it easier to apply and less likely to fall to pieces. Trust me, this is a fool-proof way of keeping your eye pencil intact!
Choosing a great quality eye pencil is also important. I am a massive fan of the KIKO Kajal Pencil (£4.20 kikocosmetics.co.uk). It is affordable, highly pigmented and long lasting.