Logon trigger that wont block connections if it fails?

I have a logon trigger that I use to track who is accessing an instance.  When someone logs on, I simply throw some info into a table.

If there is a problem for whatever reason, the trigger will fail, and no one will be able to connect to the instance until I log on using the DAC and disable the trigger.

Is there a way to code a logon trigger so that it won't block connections if it fails?