I notice users have been complaining about this not working properly for a few months at least. It's beyond high time Google fixed it.
Some users stated they had to delete their accounts and then set them up again with new settings. That's a bad work-around, not a solution, and unacceptable to some users. The solution can only come with a new Email application that can delete Trash messages efficiently, or automatically does so in the background.
I have the same problem. I'm using a Samsung Captivate, running Android 2.1-update1.
The problem is on the Android "Email" application. When I delete messages, they go to the Trash folder. This folder contains hundreds of emails and it is very slow to delete emails from there. It never happens automatically.
It is possible to delete items from this folder, but the process is VERY slow. I have found that when I open the Trash folder and select [menu] [Delete All] this does not work well at all. I do think that it DOES start deleting emails, but it seems to take several seconds to delete EACH email. If you have hundreds, as I did when I originally started cleaning out the folder, it can appear that nothing is happening at all for a long time.
If instead you check the boxes for a few at a time, you can see them disappear one at a time, with a significant delay between each deletion. It's hard to imagine how this could have occurred unless either the programmers inserted an intentional wait or are doing something else that's horribly inefficient.
I'm going to try selecting [Delete All] and leaving my phone alone for a good long time. Maybe it will delete everything (eventually). Whether it does or doesn't, I'll report back.
It turns out that Delete All does work. It's just so slow that most users probably thought it wasn't working. I suggest leaving your phone on the charger while you do it because I suspect that it you don't do so, it will go to sleep and never finish the task.