Hi Thom..
Second JOIN condition not valid due to database_id field not available in sys.dm_exec_sessions,  

USE master;

GO

SELECT GETDATE() AS date_time,

--d.[name] AS DBName,

COUNT(c.connection_id) AS Connections,

s.login_name AS LoginName,

c.client_net_address AS IPAddress

FROM sys.dm_exec_connections c

JOIN sys.dm_exec_sessions s on c.session_id = s.session_id

--JOIN sys.databases d on s.database_id = d.database_id

GROUP BY s.login_name, c.client_net_address;

working and get result each IP address have total number of connection after commended JOIN statement

Thanks