The consensus is that getting your cedula replaced can be a real pain in the neck. Most residents recommended carrying a laminated color copy of your cedula with you whenever possible and keeping the original safely in storage. However, some caution that when entering or leaving the country, an original cedula is required.
If your cedula is lost, most suggest that you contact an attorney to help guide you through the process of getting a new one as it can be a rather long and tedious ordeal. A stolen document report must be filed with the police and various applications must be filled out at different offices in Quito. Needless to say, you will want to take every precaution to avoid losing or having your cedula stolen.