In case of Remote Publishing:
The maximum amount of data that the Liferay portal can publish to live in one attempt is 2GB. This is because the data is copied to byte arrays, which cannot exceed 2GB.
LPS-35317 for more information.
This information needs to be listed on http://www.liferay.com/documentation/liferay-portal/6.1/user-guide/-/ai/lp-6-1-ugen03-staging-and-workflow-1. Maybe it should be mentioned in the "Enabling Remote Live staging" section, for example.
Please note, this limitation also affects LAR export.
It was probably not discovered before, however nowadays it's easier to have a LAR bigger than 1GB even when publishing daily, so we may have users come across this limitation.