Little info to go on , but one thing that comes immediately to mind is that a lot of SQL instances are set up without a Service Principal Name (SPN) and the connections get made using NTLM.
From my own experience in a SQL Lab, as the load test increased the load, the NTLM connections became a real bottleneck within the system - swapping it to Kerberos which allows the security token to be cached removed the login problem instantly, since it reduced the number of trips to AD for the whole solution dramatically.