Add a confirmation message on the password changing page saying "Your password was changed!" or something to that effect in order to notify the user that it was successful.
I just went to change my password, and nothing happened when I tried to change it. I tried again, and nothing happened again. It looks like it worked the first time, but there was no confirmation clarifying as such, nor was there a notification telling me it didn't work the second time. It's just a minor thing, but it's vital to prevent confusion!
Customer support service by UserEcho