Can't email a certain PDF in iBooks
There seem to be a number of people on various forums in your same boat, dating back even to when the iBooks app was first introduced. The only theories I was able to find explaining why this might be happening (large PDFs, file protected PDFs, non-searchable PDFs) are all easily disproven. So I can't help you there.

However, if all you're trying to do is get the file out of iBooks and into your Dropbox, this is doable with the help of a computer. I've included instructions for two methods below. If you have a Lightning to USB cord and a computer that you use iTunes on, it's probably easiest to transfer the file the first way. If not, you can also do it wirelessly with iCloud Drive.

If you don't mind buying software, you can also accomplish this with a third-party computer program such as iMazing or PhoneDisk.

iTunes

Connect your iPad to a computer using a USB cord (or Sync over Wi-Fi, if you have that set up) and open iTunes. Wait for the device icon to show up near the top left of the window, near the &lt;> buttons. When it does, choose File > Devices > Transfer Purchases from [your iPad's name].

Unfortunately, depending on how much content you have on your iPad, this may be fairly overkill... using this method will sync all purchased content from the iTunes Store to your computer, as well as "all podcasts from your device's Podcasts app and copies of all PDFs, books, and audiobooks from your device's iBooks app" (source).

Once the transfer is complete, your PDFs and other ebooks will appear in the Books app on your Mac, and you can drag and drop the file into Dropbox or wherever else you want it.

iCloud Drive

First, you need to make sure that the following things are set up properly, both in iCloud settings on your iPad (Settings > iCloud) and on your Mac  ( > System Preferences > iCloud):


You are logged into iCloud
iCloud Drive is turned on
iBooks is turned on within iCloud Drive settings


Having checked that, open iBooks on your iPad and wait a moment. If there is a cloud icon in the top right, that means it's busy syncing your documents. (You can tap on it to see what it's currently syncing.) Wait for it to finish.

Now open iBooks on your Mac and wait patiently for the PDF to appear. Make sure that View > Hide iCloud Books is not ticked.

Once the PDF is synced to your computer, simply drag and drop the file into Dropbox or wherever else you want it.

Note that this method can be a bit temperamental and may not work, even if it seems like everything is set up correctly. If it doesn't, and this is your only option, try rebooting your devices and follow the steps again.