Thank you for the report, @Andrew_Stein!
To start, may I kindly ask that you please provide a brief description of your current setup using this link as a guide.
Make sure to describe your network configuration/topology, including any networking hardware currently in use, so we can have a clear understanding of how your devices are communicating.
As @wizardofoz suggested above, I would recommend power cycling your Core machine and networking hardware to see if there is any improvements here.
Are you utilizing any antivirus or firewall on the Core machine? If so, try disabling.
Do you have any other remote devices that are exhibiting the same behavior? Or is it just this iPhone remote?
-Dylan