Unchecking layers in web map >> they don't check/uncheck immediately. sometimes it takes a couple minutes to reflect in the dialog area.
In all access points? on all machines? (just to rule out server issues and machine issues)
Are they excessively busy or large? (some specks would help)
Can you share the problematic web map? Additionally, try using web debugging tools like developer tools in chrome or fiddler to see there are any problems with the web requests.
Also, feel free to contact support to look into the specific issue further.
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