Last week while deployment we faced an issue in people picker. We needed to give permission to the users site from different domains. But it failed to resolve entities from a domain while other’s are working fine.
When working on this issue, we got a suggestion from a Microsoft support team. Create a security group in the frontend server and add the required users to it (Here you will get all the users from every domain). Use this group to give permission in the SharePoint site.
Of course this is a better way and Microsoft suggests this way of adding user permissions which mostly we fail to do.
But investigating more on this why this issue have occured for only a domain we found there is some issue with the network. For people picker to work we need some ports to be open from the other domain. Here is an article reading about it.