Have to login to each site

Something is wrong. I have 2 multisites that were migrated to a new host. One works normally. The other one, I have to login, as superadmin, to each sub-site. I login to the main site as superadmin, but when I try to go to the dashboard of any of the other sites, it takes me to that site's login page. I login there as superadmin and I'm in. From there, I can still see the list of "my sites" and still go back to the main site or the network admin, but again, if I try to go to another site's dashboard, it takes me to that site's login page. The host told me I would have to login to each site like that and it would set a cookie and then I wouldn't have to do it again. But I access the sites from several different computers and have to go through all that each time. Plus, it shouldn't work that way. What could be wrong?