1) Your workflow is most likely stopping due to exceptions because your .config file is not right. Note the changes:
2) You've to flush the listeners, otherwise they won't be written. You can do it in two ways.
Explicitly call Flush method on your logger variable using again InvokeMethod activity.
OR
Turn on auto flush on config file:
....
That being said, I don't know if you're aware of Workflow Tracking and Tracing capabilities. It looks a good fit for your needs. Check this answer for more links and examples.