MySQL - MySQLDump problems with large table
Your problem stems from network. In this instance, it is not the buffer used for data transmission over the network. It is the length of time the network tries to keep alive in so doing.
Please note these options:

net_read_timeout (Default 30) : The number of seconds to wait for more data from a connection before aborting the read. When the server is reading from the client, net_read_timeout is the timeout value controlling when to abort. When the server is writing to the client, net_write_timeout is the timeout value controlling when to abort. See also slave_net_timeout.
net_write_timeout (Default 60) : The number of seconds to wait for a block to be written to a connection before aborting the write. See also net_read_timeout.

You have a busy server and, at some moment in time, the data you need to read for the mysqldump to continue times out.
What I have done in the past is run the following on both source and target servers:
mysql&gt; SET GLOBAL net_read_timeout = 31536000;
mysql&gt; SET GLOBAL net_write_timeout = 31536000; 

Then, go run the mysqldump.
Setting these values very high forces the mysqldump DB Connection to wait a long time for data to be shipped over. In case you are wondering, The number 31536000 is the number of seconds in a year (365 * 24 * 60 * 60). The mysqldump DB connection will just have to stay around and wait, even for your busy server, until data comes (eventually). Please see my post from Jan 12, 2012 : Client times out, while MySQL query remains running?
GIVE IT A TRY !!!
UPDATE 2018-01-04 09:53 EST
I noticed your comment just now
Please note the error message you got from the mysqldump:

Error 2013 - Lost connection to MySQL server during query when dumping table responses at row 12891212

Please take note of the row number 12891212. If that row number comes back in the error message every single time your mysqldump fails, then maybe you can suspect data corruption. However, if your get a different row number with every mysqldump attempt, this suggests mysqldump connection is able to move along the large table and just timeout and some random point.
Please go set those values and try the mysqldump again. Then, come back back tell us what happened.