The reason hence must be "I have several people working (each on separate posts) in the system at once,"
See, if you have many people editing that post, and one removes the RFG "xy", now you edit it shortly after or simultaneously without refreshing the data, the removed RFG still figures for you as existing.
Trying to remove it though will refresh the data and fail to remove it, resulting in the error.
That, at least about the error you mention here:
https://toolset.com/forums/topic/posts-sometimes-wont-save/#post-1214848
(I noticed that when I went to remove some repeating field records, it gave me a popup error about a "System Error" )
The issue here (https://toolset.com/forums/topic/posts-sometimes-wont-save/#post-1214922) is the issue about "I can get into a certain condition where the Save Draft, Preview, and Publish buttons will not work"
We have 2 issues here, and the first for me is clear, it's due to someone else removing the RFG and the other party trying straight after to remove it.
The second issue (I can get into a certain condition where the Save Draft, Preview, and Publish buttons will not work) is as you stated due to the required fields, which give you no feedback if collapsed. We have had similar problems with "normal" fields in past and improved that, it seems, the Developers missed the collapsed case.
I can replicate this easily and escalated this as a usability issue. We should warn about the requirement (or any failure, that is) even if the group is collapsed. The error is there, BTW (see string within the group), it's just not scrolling to the field and does not expand it, instead, clicking save just "does nothing".
If we look at "simple fields groups" we see that it does correctly interrupt saving, scroll to the field and even expand, if the group is collapsed.
Thank you for the information you gave, it helped a lot