Googlebot cannot access my site but web browsers can

I had a site indexed and searchable for several years, recently something changed and I followed the tips on Google for adding 'canonical' links and redirecting from HTTP connections onto HTTPS ones etc. but still Googlebot will not access it. I contacted Google but got this response:

Thanks for your report. While your site can be accessed via a browser, Googlebot is unable to access it. This could be due to a protection system that's blocking most requests to your site. Please reach out to your hosting service provider to check what's the underlying issue and fix it to avoid further access issues. Thanks, Michel The Google Search Central Support Team

I cannot find anything on Heroku's site so I'm looking for reasons why Googlebot cannot access a site where as a web browser has no problems.

My site does not have a robots.txt or any other blocks.

Thanks.