I have just installed version 1.3.8 and the recent security patch security_patch_v138_20090619 and I am having the same issue.

This window pops up -
Send this information over an insecure connection?
Although this page was loaded over a secure connection, the information you have entered will be sent over an insecure connection, and could easily be intercepted by a third party.

I click send and then I am redirected to the Admin Home page. When I go back to the item that I tried to edit the changes did not take effect. I this case I was trying to load a custom template. I have see the same message when trying to make changes with no visable effect.

One exception to "no visible effect", I tried to add a tax zone via Locations/Taxes >> Zones Definitions >> Insert button. I type in my zone name and discription and click Update button. A blank zone is created with no name or discription. When I try to edit the zone - no chage.

I haven't looked into it too much beyond what I have mention. I access the admin through ssl. I will check for errors connecting to the db, but have no reason to think that is the problem atm. No errors in the server log. I will look in some other logs shortly.