So I pay the highest membership tier.  I buy books from the app.  I even buy digital copies of the books I have in hard copy.  I download them onto my devices and I keep them updated.

Then I’m playing in a pub with poor internet reception.  The app won’t even load, and I’m stuck with none of the resources I’ve paid for.

Is this a bug or a feature?  Cos it’s certainly teaching me to make up my own campaigns on the spot rather than buying new content.

Is there any way around this?  Alternatively, could WotC allow offline access to purchased materials?  Does anyone else have this problem?

I'm guessing a bug because the app is completely designed for viewing the downloaded content offline. I haven't used the app in weeks. I just now turned my phone to airplane mode to cut off all net connections. I opened the D&D Beyond app and can view all my downloaded sources and stuff without any issues whatsoever.

Samsung Galaxy A50.

I just tried it too....airplane mode, app came up just fine with all my books i had downloaded.  

Samsung Galaxy S20 FE

This sounds like a bug, maybe OS or hardware dependent? The app is designed to run offline.