When setting up and configuring a BizTalk environment you will also add the necessary Active Directory groups to allow access for different accounts to the platform.
In most cases, you will not touch these groups again, but there might come a time when you remove and add the groups with the same name within Active Directory. Doing so will change the SID of the group and it will no longer match the SID stored in SQL Server for the Login.
Trying to access the BizTalk Server Administration Console as a BizTalk Server Operator will for instance yield the following error when the corresponding AD group has been recreated:
You will get an error saying "BizTalk Server cannot access SQL Server. [...] Access permissions have been denied to the current user. [...] Login failed for user [...]".
You will also notice a logged error in SQL Server saying that "Login failed for user [...] Reason: Could not find a login matching the name [...]"
When looking at both the Active Directory accounts/groups as well as the SQL Server security settings, everything will look ok.
In order to correct this, you will have to remove and then add the corresponding Login in SQL Server. This might also cause you to have to delete and then add the corresponding User in the different BizTalk Databases (in general the BizTalkMgmtDb, BizTalkDTADb and BizTalkMsgBoxDb). This will also be notified by SQL Server when removing the Login.
After doing these remove/adds in SQL Server, you should be able to access the resources as expected.
Note that this is documented briefly in the Troubleshooting BizTalk Server Administration page on MSDN, but you more or less have to know where/and for what to look in order to find it.