Yes, applications for green card renewal may be denied for various reasons. Some of the most common reasons include: criminal offenses, lying on immigration applications, previous orders of removal, or using the wrong application. Read Green Card Denied.
If you have been arrested or convicted of a crime, you should always speak to an experienced immigration attorney before filing I-90 for your green card renewal. Although speeding tickets and other moving violations are insignificant, felony crimes and some misdemeanors can be problematic. Read Renewing a Green Card After an Arrest.
When a green card renewal application is denied, you may submit a motion to reopen or a motion to reconsider with the same office that denied your application. For the best results, however, you should always speak to an experienced immigration attorney.