WordPress “forgets” login password after each session

Hello, a peculiar problem has arisen:

Each time I try to log in to the wp admin panel, the site refuses to log me in.
I need to reset the password, which then emails the password reset link to me, and then I can log in again, but the next day, the same thing happens. This is true for all 4 accounts we’ve set up with the site.

Once I am logged in, everything works as expected, changes are saved etc., but then when the session has ended, the same thing happens the next time I try to log in.

The same setup worked fine on the staging server, this problem appeared after moving the WP site to a new hosting server.

Any clues anybody??

Thanks!