Problem tracing Error: 8623 with extended events
Thanks to Ronen Ariely over at MSDN and Jonathan Kehayias article on SQL Performance I was able to solve the problem. The problem was that event size was to big so that it was dropped. You can check this by querying sys.dm_xe_sessions as e.g.
   SELECT
   s.name, 
   s.total_regular_buffers,
   s.regular_buffer_size,
   s.total_large_buffers,
   s.large_buffer_size,
   s.dropped_event_count,
   s.dropped_buffer_count,
   s.largest_event_dropped_size
FROM sys.dm_xe_sessions AS s;

If any event has been dropped you will se the number of dropped events in column dropped_event_count and the max size of any dropped event in largest_event_dropped_size. If this value is larger that the regular_buffer_size then you need to increase the regular buffer size.
This was the case for me and when I did change the Max Memory size from the default to 64MB the regular buffer size was increased so much that I was able to catch the error!
As a side note the problematic query was a entity framework generated SELECT with an huge (&gt; 38 000 values) IN clause! No wonder that the database engine got enough.