I kept poking around and found some tidbits around the file being locked in a few other forums. Have you tried adding
<lockingModel type="log4net.Appender.FileAppender+MinimalLock" />
To your <appender>
element in the web.config file? From the Apache docs
Opens the file once for each AcquireLock/ReleaseLock cycle, thus holding the lock for the minimal amount of time. This method of locking is considerably slower than FileAppender.ExclusiveLock but allows other processes to move/delete the log file whilst logging continues.
As far as the performance considerations, I suppose you would need to test if this will affect you or not as I am assuming it really depends on how often you are writing to the log file as to how much this will impact performance. I can't believe that getting/releasing a lock could take all that much time though.