So the plugins to be updated are downloaded and pass verification. Then one is presented with the screen where an update to the DB should take place. It's at that point the update to the plugin(s) fail. Is that a description of what's happening?
Could be the DB user setup for the Moodle and Moodle DB doesn't have priv's it needs to finish the DB update step.
So, here's something to try:
Edit the config.php file of the site thusly:
// $CFG->dbuser = 'moodleuser';
$CFG->dbuser = 'SUPERuser';
// $CFG->dbpass = 'moodleuserpassword';
$CFG->dbpass = 'SUPERuserpassword';
The // comment out the lines for the normal/regular moodleuser and the normal/regular moodleuser password.
The active lines ... those without // in front would then be used.
Then save the config.php file. No need to restart any services, just navigate to the updates.
If you have multiple plugins to update at once, depending upon which plugins, some push you to an update screen for selecting new options for the updated plugin. Now I know at the bottom of that screen the recommendation is to update them all at once, but I've seen a combo of plugins to update get messed up at that point and the update doesn't finish. I know there are quiet a few to update, but suggest updating one at a time (ignore updating all at once) to see which ones present you with additional configuration after update and make note of them (for the next time, you are aware of which behave like that).
If you are successful upgrading that way, consider checking into the priv's of the moodleuser on the moodle database and increase the allowances.
See http://dev.mysql.com/doc/refman/5.7/en/show-grants.html for how to on priv's. Link might say 5.7 but think the grant command works the same way in older versions of MySQL.
Comment out the SUPERuser lines in the config.php file to get things 'back to normal'. And once things are 'normal' you could remove those lines from config.php.
Also check the ownerships/permissions on moodledata/mdeploy ... if on linux/CentOS/RH family:
drwxrwsrwx 5 apache apache 4096 Mar 16 2015 mdeploy
On a functioning server (ie, mdeploy works), one should see something like this in moodledata/mdeploy:
drwxrwsrwx 24 apache apache 4096 Jul 11 06:47 archive
drwxrwsrwx 2 apache apache 4096 Jul 11 06:47 auth
-rw-rw-rw- 1 apache apache 16931 Jul 11 06:47 mdeploy.log
drwxrwsrwx 2 apache apache 4096 Jul 11 06:47 var
The mdeploy.log will give info on the progress of all that have been updated ... looks like this obscured example:
2016-07-11 06:47:27 === MDEPLOY EXECUTION START ===
2016-07-11 06:47:27 Successfully authorized using the passphrase file
2016-07-11 06:47:27 Plugin upgrade requested
2016-07-11 06:47:27 Downloading package https://moodle.org/plugins/download.php/11077/repository_coursefilearea_moodle30_2016041801.zip
2016-07-11 06:47:27 Using operating system CA certificates.
2016-07-11 06:47:28 Package downloaded into /xx/xx/moodle28data/mdeploy/var/40c70d016e450a7f2733f70fd6813082.0.zip
2016-07-11 06:47:28 MD5 checksum ok
2016-07-11 06:47:28 Current plugin code location: /xx/xx/xx/moodle28/repository/coursefilearea
2016-07-11 06:47:28 Moving the current code into archive: /xx/xx/moodle28data/mdeploy/archive/coursefilearea_1468237648.0
2016-07-11 06:47:28 Package successfully extracted
2016-07-11 06:47:38 === MDEPLOY EXECUTION START ===
2016-07-11 06:47:38 Successfully authorized using the passphrase file
2016-07-11 06:47:38 Plugin upgrade requested
2016-07-11 06:47:38 Downloading package https://moodle.org/plugins/download.php/11530/filter_generico_moodle31_2016061200.zip
2016-07-11 06:47:38 Using operating system CA certificates.
2016-07-11 06:47:38 Package downloaded into /xx/xx/moodle28data/mdeploy/var/387c19a882e297f5438f2f2bce92aa26.0.zip
2016-07-11 06:47:38 MD5 checksum ok
2016-07-11 06:47:38 Current plugin code location: /xx/xx/xx/moodle28/filter/generico
2016-07-11 06:47:38 Moving the current code into archive: /xx/xx/moodle28data/mdeploy/archive/generico_1468237658.0
2016-07-11 06:47:38 Package successfully extracted
The other piece to this that might be giving you grief has to do with an http server (yours) talking to an https (moodles) server.
To assist with that issue one can put at moodleorgca.crt file at the root of your data directory.
https://docs.moodle.org/24/en/SSL_certificate_for_moodle.org
'spirit of sharing', Ken