I know this thread is old, but I wanted to chime in with my own 2 cents.

I have also had the issue that many have described here - When I change the axis within a group, sometimes it seems to reset later.

Note that the above comments are right - right-clicking to change the axis is a temporary change. However, the axis tool will permanently change the axis... unless you run into the issue being discussed here.

I have found it seems to be an issue with saving. If the model is saved in ANY WAY (autosave or manual) while you are still in the group in which you changed the axis, the axis change will be discarded upon saving the file. You MUST back out of all groups and save there. In this way, the axis change will stick.

It is extremely frustrating, particularly as autosaves apply to this as well. I just get in the habit of whenever I change the axis in a group, immediately back out to the main model and save. Then it sticks.

I suspect the issue mentioned directly above regarding importing is a similar thing - I would hazard a guess that SketchUp is saving the file when you are importing as a failsafe, and thus screwing up the axis.

Now, seeing as this issue was first brought up five years ago, it would be swell to actually see a fix for this... But as there are many feature/bug requests that I have seen that are years and years old with no fix or address, I wouldn't hold my breath.