The JDBCAppender holds a single database connection for all its logging. If that database connection is closed, it does not attempt to make a new connection.
Many connection pools automatically close connections after a certain amount of inactivity. (This can be worked around by properly configuring a pool).
Database connectivity issues are also common enough that a long running application may experience temporary network issues. When the network comes back online, the logging will not resume.
I've been meaning to submit a patch for this, but I haven't gotten to it. Since I saw that you are looking to come out of beta soon, I thought I would log this issue in case someone else has time to write the patch before I get to it.