I was unable to find Ralf's emails in the list other than one note that
it should be fixable by changing mysql's my.cnf.

Looking at doc/mysql.txt, a fix for this is condition to change the
max_allowed_packet size setting. See also:

  
https://stackoverflow.com/questions/7942154/mysql-error-2006-mysql-server-has-gone-away

which indicates it could also be an out of memory condition, connection
limit or a timeout being hit.
The interactive_timeout and wait_timeout values are by default: 28800
seconds or 8 hours and the entire run
takes only 20 minutes. There are no settings for these vars in my.cnf
that would reduce the value.
Max_connections is 151 by default, again I don't think this is an issue.

I tried to edit /etc/mysql/my.cnf change that to 500M (from 16M) and
restart the server. This seems to have been done correctly according to
the log:

 https://travis-ci.org/roundup-tracker/roundup/builds/504322490

see lines: 5851 and 5927

but the 14 errors are still there.

Looking at the errors, some look like an example of issue2550743 as
these failing tests are indexer based:

test/test_indexer.py::mysqlIndexerTest::test_basics FAILED             
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_casesensitity FAILED      
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_change FAILED             
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_clear FAILED              
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_extremewords FAILED       
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_manyresults FAILED        
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_stopwords FAILED          
 [ 28%]
test/test_indexer.py::mysqlIndexerTest::test_wordsplitting FAILED      
 [ 28%]

but these failing tests/errors:

test/test_mysql.py::mysqlSessionTest::testDestroy FAILED               
 [ 65%]
test/test_mysql.py::mysqlSessionTest::testGetAll FAILED                
 [ 65%]
test/test_mysql.py::mysqlSessionTest::testList FAILED                  
 [ 66%]
test/test_mysql.py::mysqlSessionTest::testSetSession FAILED            
 [ 66%]
test/test_mysql.py::mysqlSessionTest::testUpdateSession FAILED         
 [ 66%]
test/test_mysql.py::mysqlSpecialActionTestCase::testInnerMain FAILED   
 [ 66%]
test/test_mysql.py::mysqlSpecialActionTestCase::testInnerMain ERROR    
 [ 66%]

aren't AFAIK indexer based.

The errors always come from:

    def sql_close(self):
        self.log_info('close')
        try:
>           self.conn.close()
E           OperationalError: (2006, '')
roundup/backends/back_mysql.py:589: OperationalError

So I am stumped.