It seems that on backup resume, Areca will ignore any backup filters in place.
Originally, I was not aware that Areca would attempt to backup a protected system folder (System Volume Information), so once it ran in to that issue of it being denied to standard processes, I went at trying to add it to a filter to be ignored. However, no matter what I try, when I resume the backup, Areca attempts to back it up anyways as if I had never added it to the list. Here is my filter list:
<filter_group logical_not="false" operator="and" >
<directory_filter logical_not="true" directory="F:/System Volume Information"/>
</filter_group>
As you can see, I have completely done away with all other filters (ignore file extensions .tmp, .temp) in order to troubleshoot this problem. With that filter, Areca will still attempt to backup any file within System Volume Information, which I feel is a direct contradiction to this filter.
To anyone else who is experiencing this issue, I wanted to post a potential (and dangerous) work around. If you take ownership of the System Volume Information folder (as your own user) and restart your computer, Areca will be able to continue backing up that folder, even though you've already added it to your exclusion list.