Intermittent failures to connect to 127.0.0.1
Since this question is already quite old, I won't bother asking you to clarify the problem, and will instead try to focus on providing some things that might be worthwhile looking at, that some future visitor might find helpful.


Microsoft .Net Framework 4.5 and 4.5.1 have a known issue with connections to localhost
It's possible your server is suffering from thread-starvation.  Confirm the maximum number of expected simultaneous connections, including pooled connections that might not be actively performing tasks is below the maximum number of threads for your server.
Confirm there are no network-related filters in place that might be dropping connections.  Running netsh winsock show catalog will show the base service providers and any layered service providers that might be interfering with connectivity.  Particularly look for anti-virus or firewall apps.
Check network utilization, and if necessary tune networking parameters for performance.
If SQL Server is running in a virtual machine, check the host server to ensure a memory reservation has been set that prevents memory being swapped out (VMware, Hyper-V).  Ensure a CPU reservation has been set to prevent the virtual machine being starved of processing power.