[Geschlossen] Translations done using ATE do not always get applied on live site

Background of the issue:
We have a common, but still intermittent issue that when we use the ATE to update certain pages on our site, the changes that we make in the ATE are not reflected on the live site. Sometimes going to WPML->Support->Troubleshooting page and clicking "Synchronize local job ids with ATE jobs" or "Synchronize translators and translation managers with ATE" resolves the issue. Link to a page where the issue can be seen: versteckter Link

Symptoms:
The changes made in ATE are not reflected on the live site. Sometimes we see a continuously spinning circular arrows icon, or just the gear icon in the edit translation column of the page listing. For some pages, we always see the gear icon in the translation column on the page listing, even when we have just fully updated the translation. This is most frustrating when we have incorrect information that does not get updated on our site.

Here is a Loom video that demonstrates the gear icon not disappearing: versteckter Link

Questions:
Why are the changes made in ATE not reflected on the live site?
What do the continuously spinning circular arrows icon and the gear icon in the edit translation column indicate?
Why do some pages always show the gear icon in the translation column even after updating the translation?
Are there any other steps we can take to ensure that translations are applied correctly on the live site?