Time Machine is not backing up Dropbox folder. Can this be done?

There are a couple of other questions and posts regarding Time Machine and Dropbox in these forums, but they do not seem to address the same thing I am experiencing.

I am using Dropbox (v 1.2.52) on my mac (mini, osx 10.6.8) and have some shared folders, and other items in there (regular Dropbox usage - pictures, plain-text files, MS Office files, etc, etc,). Recently, I bought a hard drive to serve as a time machine backup disk. I connected the drive and started Time Machine. My entire system was backed up to the new, external disk. Great, everything going as expected so far.

Fast forward a few days. I check to make sure everything is working correctly. Changed items in my Desktop and Home folder are appearing in Time Machine as I expect. However, items within my Dropbox folder (which _should_ act as a regular folder) are not reflecting any changes in the Time Machine backups. My Dropbox ( ~/Dropbox/* ) folder is appearing as a static version of when Time Machine initially backed up my system.

I have not tried reproducing this, but my steps thus far have been:

1) Install / use Dropbox (w/ shared folders)

2) Start/initialize Time Machine.

3) Change/add/remove items in the ~/Dropbox folder and let Time Machine do a regular backup.

4) Change will not appear in the Time Machine "snapshot", but still be on the system (i.e. "Now" snapshot shows the changes, but backups from the previous minute/second will not)

Other posts have mentioned that Dropbox can put a lock in a file that prevents backup and specifically this could be MS Office files. I am working with plaintext files, so this rules out Office file locking. I have closed all the files (or rather programs accessing those files) from my system, but this did not affect the backups. I have paused Dropbox syncing, but time machine backups were not affected. I have quit the Dropbox program, but Time Machine backups were not affected. I am really not sure what is going on. Has anyone else experienced this? And, how can I get Time Machine to backup my Dropbox folder?