Why can not I delete messages from my IMAP account on my iPhone 4?
Maybe the trash folder is not appropriately set on your iPhone.
Relying on the email - carrier, you might need to pick the proper "removed" folder in your account setups on the iPhone.
(possibly the translations are not essentially, i am making use of a German iPhone) : Go to "Settings" - > "Mail, calls ...", pick your IMAP account, pick "account details", consider all-time low and also pick "progressed".
Below you can pick which folder is your trash folder.