While researching further, I found the following information on another site:
"I believe that that the external USB drive must be formatted either Mac OS Extended (Journaled), or FAT (not exFAT) to work with the Airport Extreme (or Time Capsule). I saw this on an Apple support page, http://support.apple.com/kb/HT2426
Note that even if you format the drive as Mac OS Extended (Journaled), once it's plugged into your Airport Extreme even Windows machines on your network will be able to read/write to it. It's because the SMB network protocol is being used so the Windows machines never actually see the format of the drive. So, the only reason I can think of to format FAT or exFAT is if you are sometimes going to unplug it from the Airport and plug it into a Windows machine directly."
I don't plan on connecting the drive directly to a windows computer (USB), so I plan on re-formatting the drive to HFS+ and I'll report on what happens.
I'm happy to report that, after reformatting the drive to HFS+ (aka Mac OS Extended), there are no problems writing/copying large or small files to the AirDisk drive. I'm also happy to report that I am copying to the drive at a rate of roughly 4MB/s.
As I mentioned earlier, the only catch is that I am unable to plug the external drive directly into a Windows computer via the USB port as Windows is unable to read HFS+ formatted drives. (I can, however, plug the drive into a Mac computer as they can read HFS+ formatted drives. The only problem is that I don't own any Macs at this time! LOL!)
You're probably wondering how I formatted the external drive to HFS+ since I don't own any Macs. (Windows only allows you to format drives in exFAT, FAT, NTFS and the like.) That is a good question. Basically, I downloaded an open source formatting tool called, Gparted, which allows you to format any USB drive to any major file format system. Since Gparted is an open source tool, it is a little cumbersome to use. Once you figure out how to use it, it is a cinch to format the drive to HFS+. (Of course, an easier method would be to borrow a friend's mac, plug the drive into their mac, and format it to HFS+ using their mac.)
For a step-by-step guide on how to solve this problem, see the steps below:
1) Backup all data from external drive
a) Fortunately, I have a 1TB ultraportable USB drive which has enough space to backup all data on the drive
2) Format the external drive to HFS+ using one of the methods below
a) Plug it into a Mac and format it
b) Use Gparted (free) to format it
3) Plug the drive back into the Airport Extreme
4) Start copying files over to your networked drive!
I hope this helps you! Cheers!