Authenticatication on the QlikView AccessPoint is handled by Windows and forwarded to Active Directory. See Authentication (Help.qlik.com).
Possible root causes that need to be addressed:
No Trust is set between DomainA and DomainB. This will prevent users from DomainB from authenticating against DomainA.
Incorrectly configured DNS forwarders whereby conditional forwarders are made for domains. If this is not correctly configured on all domain controllers, authentication will fail.