Which platform/OS/version? Which minor Acrobat XI version? Does it want to save to the same location for all PDFs even when they come from different locations?
windows 7 pro 64 bit! adobe acrobat XI Pro! yes, it wants to save it every time on the same location, but not there where you opened it!
I do not see this behavior. I always get prompted to save in the same location from which the to-be-signed PDF came.
It is possible that there is some preference that forces saving in a specific folder but I am not aware of such preference, so most likely it does not exist. Someone else would have to provide some insight.
I followed up on this with some people who know more about saving in Acrobat and here's what I learned. When Acrobat saves a PDF it generally populates the 'Save as' dialog with the location for the saved file the same as the original file. But before it does that it checks that it can write to that location. If it cannot write to the location from where the original PDF came from, then it populates the 'Save as' dialog with the Acrobat's default location (it may be different in Acrobat and Reader and whether Reader is in Protected Mode or not). The most likely reason for your problem is that PDFs that you want to sign come from a location (like a network drive or cloud) to which Acrobat does not have full permissions.
To check that open one of your PDFs and try to "Save as" it. See if you get the same location as when you try to sign. Also, you can create a small text document in a Notepad and try to save it to the location from which your PDF came from. Se if Notepad allows you to do that.