Here's the PDF 

Here's the PNG

I even tried to recreate the shapes to see if there was something else causing the problem

Hi Adam thank you for posting in the Lucid Community! This may be a document specific issue since I'll need information regarding your account I am going to move your post to a private ticket! 

I have same problem. It looks like if you have grouped objects they do not get exported. If you ungroup them they are exported properly.

Anyway it's still the problem that you have to ungroup all oject before exporting :(

Hi @audrius thank you for continuing this thread. As this is a document specific issue I have created a ticket from your post and will be reaching out via email. 

If any other users are experiencing issues with shapes disappearing on export/download please submit a support ticket that includes the URL of your document by using this form.