If syncing has stopped working I would verify first that you are using the latest supported build of the Outlook Plugin (OPI). I understand this post is extremely old however as of 4/17/2023 the latest OPI version is 2.7.7.
Second, I would verify that your version of Outlook is on the Semi-Annual Channel. Many users want to run the latest version of Office/Outlook and unknowingly switch to the Current Channel release schedule or the Monthly Channel. We *only* support the Semi-Annual Channel so it is vital confirm you are running on a supported platform. Please refer to the following page that covers the Plugins Supported Platforms.
https://support.sugarcrm.com/Resources/Supported_Platforms/Plug-ins_Supported_Platforms/