Password change does not stick

I have had this same problem over the last week. 

I noticed that my password no longer was accepted as valid, so I went through the standard password change process, with success. I also changed the password on my handheld device, and was successful. Everything is by the book to this point. 

Flash forward about 24 hours. My password is no longer valid on any device, and not valid when I log in using the web interface. Go through the password change process again, and everything is fine for another 24 hours.

Support has offered no solutions at this point. This is getting tedious. Any suggestions?