You can add the domains for these sites to Trusted Locations: Edit->Preferences->Trust Manager and click on "Change Settings". Make sure that you do that for sites that you really trust.
In Acrobat 11 Pro "change settings" has three options, "Allow PDFs to Access All Websites", "Custom Setting" and "Block PDFs' Access to All Websites". Under "Custom Setting" it is true that one can enter specific sites at trusted in that access is allowed. Also, the options for sites not listed as trusted sites are to "Always Ask", "Allow Access" and "Block Access". However, even when I bypass "Always Ask" and choose "Block Access", Acrobat opens a dialog box and notifies me when it blocks access to one of the sites not on the explicitly trusted list. Acrobat does this every time and each time I have to manually close the dialog box to continue scrolling through the pdf. I may not have made it clear, but I do not want to be notified that Acrobat has blocked access to a site and to have to interrupt what I am trying to do by manually closing the dialog box. If I wanted any notifications I would have chosen "Always Ask". I hope that my issue is now more clear. Your suggestions are well taken, but do not address the problem. If you have any additional ideas I will be glad to see them and I appreciate your trying to address my question.