Error using Microsoft SQL server

Where I work, we are all on active directory and we use our Domain credentials to log into everything. Every user is added by "use windows authentication", with the correct name and domain. The serverPC is here in the same building, reachable with mainpassword of the database.
All users will have to add the datasource, checked 'integrated sercurity'. This worked one time, for an hour. Then it stopped wordking, giving the error message:
The current datasource is unavailable.
Login failed. The login is fron an untrusted domain and cannot be used with Windows authentication.
Do you have a solution, I can't give the wanted rights to my collegues this way.
Thanks.