I had a similar problem.
Win7 x64 / bfgminer 3.10.0 x64
I have 2 devices; ASIC Block Erupter and ANT U1
My ASIC was mining just fine, running from a CMD script in F:\Crypto Coins\Miners\BFGminer\bfgminer-3.10.0-win64\asic.cmd
Then I got an ANT U1 today, plugged it in, ran a CMD script from the same folder as above, and got "Do not have user privileges required to open COM3". For a few minutes it was mining (Accepts) but then everything turned to "Rejects".
I moved my BFGminer folder to F:\bfgminer and ran the ANT script as Administrator. Am still getting the "Do not have user privileges required to open" error but no more rejects.
The ASIC script, ran from this new folder location, still works as it did before (no difference to performance etc).
So my guess is there is something in the BFGminer code logic that is slightly different between ASIC and ANT processing.
ASIC.CMDbfgminer -S erupter:all -o stratum+tcp://de1.miningpool.co:10701 -u mfread.asic1 -p x
ANT.CMDbfgminer -S antminer:all -o stratum+tcp://de1.miningpool.co:10701 -u mfread.ant1 -p x
(yes, I could run both devices off the one CMD line, but from time to time I like to run each one against a different pool, and yes I know I can up the clock rate on the antminer to give a better performance than stock-standard 1.6 GH/s)
Try moving BFGMiner to a different folder, off the desktop. A similar problem (at least privilege related) and solution was posted
here (scroll up to see the original problem) and while I'm not sure that it is the same as your issue, it shows that shortcuts or files on the desktop can cause this.
I'm not saying it will work or even that it makes sense (I'm not sure why Windows would do this but he didn't post enough info to investigate further). But it's something to try and rule out. Because the desktop is a user folder Windows treats it differently than something in a non-user folder?
Anyway, put the miner's folder in a folder like C:\Miners (so C:\Miners\BFGMiner) and also put your batch file in there (you may have to edit the paths in the batch file depending on how you wrote it). Browse to the folder in Explorer and double-click the batch file and see what happens. Also try right-clicking on the batch file and selecting Run as Administrator. Also don't put the folder inside the Program Files, Program Files (x86), ProgramData, or Windows folders as that may cause additional problems.