Here are a couple of things you can try.
Exit calibre, launch iTunes with your iPhone connected. Watch the status window in iTunes to observe if there are any syncing operations with your iPhone. If so, wait until they are complete.
In iTunes Preferences|Device Preferences, enable the checkbox 'Prevent iPods, iPhones and iPads from syncing automatically'.
In iTunes, select the connected iPhone in the DEVICES list. Select the Summary tab. Under Options, enable the checkbox 'Manually manage videos'.
Restart calibre, try sending books again.
Make sure that if you are using calibre to send books to multiple iDevices, you exit calibre and disconnect the first iDevice before connecting the second iDevice and restarting calibre.
If none of these suggestions make a difference, I'm out of ideas. You can use the 'Connect to iTunes' method to transfer books to iTunes, then to your iPhone.