A fatal error occurred while creating a TLS client credential. The internal error state is 10013

Basically we had to enable TLS 1.2 for .NET 4.x. Making this registry changed worked for me, and stopped the event log filling up with the Schannel error.

More information on the answer can be found here

Linked Info Summary

Enable TLS 1.2 at the system (SCHANNEL) level:

Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2]
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Client]
"DisabledByDefault"=dword:00000000
"Enabled"=dword:00000001
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Server]
"DisabledByDefault"=dword:00000000
"Enabled"=dword:00000001

(equivalent keys are probably also available for other TLS versions)

Tell .NET Framework to use the system TLS versions:

Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v4.0.30319]
"SystemDefaultTlsVersions"=dword:00000001
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\.NETFramework\v4.0.30319]
"SystemDefaultTlsVersions"=dword:00000001

This may not be desirable for edge cases where .NET Framework 4.x applications need to have different protocols enabled and disabled than the OS does.