Adobe Reader keeps downloading: http://acroipm.adobe.com/10/rdr/ENU/win/nooem/none/message.zip

I believe this is part of the Adobe Approved Trust List program. It seems that, when Reader X starts, it downloads this file from an Adobe server. The zip file contains 3 files, the largest of which is signatures.xml, which unsurprisingly appears to contain details for a number of X509 certificates.

You can control this behaviour by selecting "Preferences" from the "Edit" menu and then going to the "Trust Manager" section. Here you can enable/disable loading these certificates, control whether Reader will ask you before updating and manually update now.

We recently upgraded about 100 Windows PCs to Reader X. Since then I can see frequent accesses to this URL in our logs - and since most of our PCs are restricted in their Internet access, most of the accesses are blocked. ZoneAlarm on my laptop has been alerting me to Reader trying to access the network every time it starts. When I un-ticked "Load trusted root certificates...", this stopped happening. I was also experiencing frequent crashes of Reader X when closing the program. Those have now stopped as well.

Packed size of the zip file is (currently) about 34KB, so I am going to whitelist this URL - it's easier than working out how to turn the functionality off for 100+ machines! However, it may be possible to do something using Group Policy. I already have a custom GP template to disable Acrobat Javascript across the company.