Service actions are not supported by ArcGIS Server. If service actions are applied to a tracking service creating a real-time tracking layer in your map, the service actions will not be published with the tracking layer.
There is no direct solution for this issue. However, depending on what your service action is accomplishing, there may be a workaround. For example, if you are using a Filter service action to filter out certain real-time data from your tracking layer, it is possible that the same data could be suppressed using a Highlight / Suppression layer action. This would result in a published map that looks the same.
Service actions operate on data messages as they are streaming into the client application, such as ArcMap, to become tracking features. When you are working with real-time data in ArcGIS Tracking Analyst, features in a real-time tracking layer are being created from the data messages streaming in from a tracking service. Therefore, service actions have the capability of modifying or deleting data contained in tracking data messages before they become features.