Given a high-throughput network and only 1 or 2 hops between any system, why would the "Securing remote connection" stage be so slow?
Sometimes it looks like the other system is asleep but ethernet power saving is off and it can never fall to sleep because Power Options are set to "High Performance".
What could cause this process to be slow if all network obstacles were removed and systems definitely not sleeping or working on anything?
Also, the domain controller is certainly not overburdened and uses less than 4% of CPU during peak hours.
41 Answer
In case your machines do not have access to Windows Update
One task of "securing remote connection" is to update the root certificate store via Windows Update to be able to verify the certificates used for the remote connection. If your machines do not have access to Windows Update, this task will timeout. Unfortunately, it will not fail immediateley, it will really timeout after about 20 seconds.
If your machines do not have access to Windows Update anyway - not commenting on that - you can disable the automatic renewal of root certificates. You can enroll this setting either by GPO or by local computer policy (open gpedit.msc):
Go to Computer Configuration > Administrative Templates > System > Internet Communication Management > Internet Communication settings and enable the policy Turn off Automatic Root Certificates Update.