On April 16 201 9Esri's ArcGIS Online transitioned to utilizing only TLS 1.2, and some clients/versions will experience a disruption of service if they do not follow the steps described in Esri's TLS_Guidance.
This Esri document also lists which clients require update/fixes to support TLS 1.2, including what Esri products and a list of older browsers.
Esri has established a support page to help customers at https://support.esri.com/en/tls.
When connecting to ArcGIS Online via ArcMap:
You may encounter the following error:
To fix this you will need to update your software with the patch as described in: Install the TLS 1.2 patch on ArcGIS Desktop.
You can also Test ArcGIS TLS 1.2 connections to ArcGIS Online.