I made a few fixes that will allow the smart axis panel to properly react to new labels. It'll work when using a datetime axis or a regular category axis.
The only catch with the category axis is that axis interval will have to be set periodically as the displayed dataset gets larger.
So, it would be something like categoryAxis.interval = dataItems.count / numberOfLabelsToDisplay 

I finally found the problem...  IGCategoryDateTimeXAxis.

I've tried changing to a regular category X axis but then I get different behavior where labels disappear unless I zoom in.

I'm no longer able to reproduce the issue after I made a fix earlier. Can you try out this sample and let me know if labels get clipped after the insert?

That looks like the problem. Thanks! :)

I think i found the issue where the label gets clipped when you only have one visible label. Before I start making any changes, though, I'd like to make sure that's the issue you're seeing with your project.

Take a look at the attached project. Once a point is added, the label is clipped. Once there are two labels, they get scaled down to fit the available axis label space.
Let me know whether that's the problem you were reporting.