Why not first repair the drive using Disk Utility?
Open Disk Utility in the Utilities folder. After DU loads select the TM hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say 'Verified' then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is 'Verified' then select your TM volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported, then quit DU.
The problem of having a TM drive revert to read-only is not new. There is this past fix:
What to do if Time Machine reports you don't have permission
This was posted in the Apple Discussions by V.K. I have only modified it slightly to be more generic.
The problem seems to be that 10.5.6 changes permissions on a file so that even the root user doesn't have write peivileges. I have no idea why they did this. The workaround suggested in [an]other post will probably work, too, but i did something less drastic. Instead of deleting the file I changed permissions on it, and it worked just fine. An added benefit is that the permission change seems to stick, so you don't have to delete the file every time you change a drive.
[Open the Terminal application in your Utilities folder. At the prompt [enter] the following command:

sudo chmod 644 /volumes/'TM drive name'/.xxxxxxxxxxxx

The name of the file .xxxxxxxxxxxx is based on the MAC address of your computer and will be different for every computer. Put the name of the TM drive in the above and keep the quotes.
You'll have to enter your admin password (which you won't see) which is normal.
This was edited by Kappy just for cleanup.
Enable Finder to Show Invisible Files and Folders
Open the Terminal application in your Utilities folder. At the prompt enter or paste the following command line then press RETURN.

defaults write com.apple.finder AppleShowAllFiles TRUE

To turn off the display of invisible files and folders enter or paste the following command line and press RETURN.

defaults write com.apple.finder AppleShowAllFiles FALSE

Alternatively you can use one of the numerous third-party utilities such as TinkerTool or ShowHideInvisibleFiles - VersionTracker or MacUpdate.
Also, see User Tips for Time Machine for help with TM problems. Also you can select Mac Help from the Finder's Help menu and search for 'time machine' to locate articles on how to use TM. See also Mac 101- Time Machine.