I am using the plugin on a live site, and it works fine. I have not had any of the said problems, so it's really difficult to say what's going wrong. Since it also happens to other payment gateways, it sounds like it's a problem with CloudFlare blocking legitimate requests.
Can you guys please do this for me and show me the results?
1. Head over to https://commerce.coinbase.com/dashboard/settings & click "Details" on your Webhook subscription
2. Send a test, the test can be anything.
Then show me what your server responds with.
Also not to forget, in CloudFlare please make a Page Rule that looks like this.. Please the webhook test before you make any changes to CloudFlare so we can confirm that it's cloudflare or what it is causing the problem.
The website should obviously be yours, however this rule will basically skip all the security rules in the application folder. This may also fix the problem for other gateways.