If you go to the log4net website, you can find some examples, at least one of which is an asynchronous Appender.
http://logging.apache.org/log4net/release/example-apps.html
Note that I have not used any of these examples, so I cannot vouch for them one way or the other.
Here is a link to the actual asynchronous appender from the log4net Examples area in their code repository:
http://svn.apache.org/viewvc/logging/log4net/trunk/examples/net/2.0/Appenders/SampleAppendersApp/cs/src/Appender/AsyncAppender.cs?view=markup
I looked at it briefly, and it apparently acts as a wrapper around one or more “conventional” Appenders. On each logging request (containing one or more LoggingEvent objects), a ThreadPool thread is used to forward the LoggingEvents to the list of wrapped Appenders.