It seems most likely you're hitting the "server busy" (503) New "Service Busy" responses beginning during high load
We don't serve many of these, though. We have a handful at 00:00 and 16:10 (just now) which are our two busiest times, and single digits throughout the rest of the day.
If you'd like us to have any more investigation, then including an HTTP error code, the ACME error, and whether the client retries 503s automatically would be helpful information.