Hi. I'm having the same issue. It just started happening to me recently. I'm on Acrobat Pro 9.1.1. To me its more annoying than a really serious issue like the fit to printable area / shrink to printable area options not working in the print dialog box.
Try repairing Permissions with Disk Utility:
If that don't work download and install AppleJack for OSX.5.
then restart in Single User mode. (Unix Screen)
at Blinking Square Cursor tye applejack and hit return when menu comes up follow 5 steps in turn.
Choice one takes a long time and if it finds something you may have to run two or three times until it says files have either been repaired or appear to be okay.
Then go through steps 2-5
Steps 3 and 4 require running for system and user.
after 5 step done, quit then restart as per instructions.
Note after doing this Computer will take a long time to get started , you might even see blue screen for a few seconds.
Applejack removes certain files and caches that have to be rebuilt.
Computer will work and seem snaper for a while.
See if this cures your opening multiple file problem. could be some minor cross-linkage of files that applejack might fix
This just happened to me this morning.
Tried the Disk Repair, but it didn't help.
Called Adobe and they had the solution. (At least for me.)
In your Preferences folder, there is a file called com.adobe.acrobat.90.sh.plist.
I was asked shut down all open programs, then drag that file to Desktop. Then, I reopened Acrobat and everything worked as normal. It also created a new version of that file.
In other words, it sounds like the original plist file was corrupt.
Anyway, cheers to Adobe for helping me painlessly get this corrected.