I just uploaded Bugzilla Helper 0.2.0. This improves on the last release by making making the submission of comments an asynchronous operation. It also uses the activity manager in Thunderbird to track the process of the submission, and retry it if an error occurs.
There are still some apparent issues with the REST API that the add-on is using, and I’ll likely include some workaround in upcoming versions. 0.2.0 is available on addons.mozilla.org and is a recommended upgrade. Current users will have to update since sandboxed add-ons do not automatically update.