Settings\iBooks - try taking the tick out of Sync Collections. Let the pad and iTunes manage the syncing operations under the following.
Settings\App store tick all items.
and in iTunes on PC - Edit\Preferences Store tab - tick Books box. and tick - always Check for Available downloads.
Connect device to iTunes via cable - then click on Library\Books in left pane. Ensure all titles are ticked. Click your device icon at the left, and in the window that appears navigate to the Book tab. Sync Books should be ticked, and Selected Books option.
Check all titles are ticked, then sync to your device - noting that two syncs may be required, sometimes three if the material category as given in the embed code differs.
when finished, check your library, arrange your collections as you wish and see how you get on from here.
In Settings\App Store, dont forget to have Allow downloads on Cellular On as well.
Note that if you save to ibooks on your ipad with these options as is, your library in itunes will update with the new titles form its internet connection - not via the devices' sync.
If you update ibooks collection with iTunes open on your PC, clicking sync will not pdate the collection. Close iTunes and reopen it. After the next sync, the books will be in your library marked with a tick, and if you browse to your devices books page (click device at left in PC iTunes, then Books tab), they will be there too ticked also.
I think that when iBooks sync is set, it makes a network call that conflicts with the ipad\itunes setting. depending on network bandwidth and method of download the library update may or may not succeed.
The operation given here has been tested at the time of writing and everything worked as it should.
Hope this may be of some help to others.
Best wishes, Ct