Try connecting to the service layers through creating a GIS Server Connection in ArcCatalog.

If this does not resolve the issue, proceed to Step #5. If you do, you may need to work with IT to add some exceptions to it.

Does the problematic network have a firewall?.

The proxy information you enter should be the same as what is set in the Windows Control Panel under Internet Options > Connections > LAN settings. Next, try opening ArcCatalog and selecting Customize > ArcCatalog Options > Connections, and entering the proxy information there. If it works, then the issue is related to the proxy server. If disabling the proxy server does not resolve the issue, move onto the next step. If yes, work with IT to try temporarily disabling it.

Does this problematic network have a proxy server?.

If the issue is machine specific (does not happen on other machines on the same network), proceed with Steps #7-9. If the issue is network specific (works on your laptop at home but not in the office), proceed with Steps #3-7. Also, if you are using a laptop, try taking your laptop home for the night and testing the workflow from another network. On another machine on the same network, test to see if the issue is network or machine specific.

Test if the issue is machine or network specific.

If you are confident that you have a good internet connection, proceed to Step #2. If you do not, you will need to work with your IT department to resolve this issue. Online services require connection to the internet, so making sure that you have a sound connection is critical.

Ensure you have a solid internet connection.

Here are our tips to begin troubleshooting these types of issues in ArcGIS for Desktop: In some cases, the Add Base Map window opens, but disappears before a base map is actually added to the data block. The options to add basemaps and data from ArcGIS Online and ArcGIS for Portal are disabled in ArcMap

Arcmap update