I would advise using the Enhanced Gmail plugin provided by BlackBerry or going to the browser on your mobile device for Gmail.
@Surya B. If you are having trouble syncing or accessing Gmail, I would advise following the steps that The C Man has proposed above. If one of those doesn't resolve your authentication issue, please post back on this thread and let us know.
@Papa Bear the end of life for Google Sync for BlackBerry will not affect the mobile browser version of Gmail or the Enhanced Gmail plugin. Both will continue working and are the two best solutions for BlackBerry users.