Solution:
Have you tried disabling the rest of the plugins?
If you don’t want to disable them, you can also prevent WordPress from including them for a little while. Just go to your /wp-content/plugins/ directory(through FTP client) and rename the directories of all plugins, except for Job Manager(for instance just add _ at the begining of all directories). Make sure not to go to the plugins page, until you’ve restored the proper directories names – otherwise WordPress will disable the plugins(whereas when the plugin files don’t exist and you’re not on the Plugins page, their files are simply not included). Then see if Job Manager is still not sending emails.
You can also try installing all of the plugins on your test server and disable them one by one to see if it’s a plugin conflict.