Power BI support has come back to me telling me it's not related to Power BI. They want me to contact the publishers of the visual. So I also raised the issue on the HTML visual Github page: https://github.com/dm-p/powerbi-visuals-html-content/issues/61
"Since Power BI Service has been udpated and this visual is a custom visual, so it may could not be shown correctly in Power BI Service."
Updated with what? We have no visibility whatsoever on what changed with each service update. So we don't know if this is intentionally (tightening security?) or inadvertently. The mere fact that the functionality still works (albeit only the first time) would hint that it is not a security improvement but rather a goof-up.
We have started running our own forensics on this but it's a lot of poking in the dark at the moment.
Currently this issue should be fixed in Power BI Service, please check it again.
Best Regards,
Community Support Team _ Yingjie Li