sorry for the latest issues and inconvenience I might have caused. @DaveE is correct: we're hitting Instagram's API authentication limit. Thanks a lot for the input and suggestions. I appreciate this very much.
I have fixed the wordpress plugin to allow you to enter your own client information. This means you'll have to register a client so that you can use it without being limited by other users of the app.
I need two more days to make this all nice and deploy it to wordpress. So by Sunday evening everything will be fine again.
For the time being if things get urgent. You might wanna use this 'instagram gallery widget': http://ink361.com/#!/promote. Scroll down to the bottom off the page, specify how you would like it and click 'get code'. Then paste this code inside a widget box on your blog.
Please stay tuned. When I have pushed everything to WordPress, I'll inform you all.
Happy photo viewing!