Can't login to a multisite after Domain Mapping 4.1 update

Hey

I have just updated the Domain Mapping plugin to 4.1 and I have started to experience login issues for our multisites.

When I visit one of our multisites and try logging in by adding /wp-admin/ to the end of the domain, I get the following error message:

ERROR: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress.

I temporarily changed the COOKIE_DOMAIN constant in the wp-config.php to match the multisite domain and it let me login, however as soon as I change it back to the root domain it stops working again.

I can login and access a multisite's dashboard by going to our root domain and logging in, however this isn't a suitable fix for our other staff members.

Do you have any advice? Please let me know what other information you need.

Many thanks,
James