I have now solved the problem. The only way I could think of was to re-install Job Manager. That was easy. There are four checkboxes in “Settings” that you should decide on before you uninstall. I asked Job Manager not to delete the jobs (there where no applications, due to the registration problem…) and it worked fine with the new and fresh installation.
I think our problem can be derived to the fact that we changed name of the site when we published it, from a www2 address to a normal www address. The Job Manager stopped working after that change.