Oops, my mistake!
I tried with some historical data, and used absolute times in the time picker. I actually do see this now, and I'm still using Kibana 5.5.0.
I could get it to happen when I'm looking at a time window of 2-5 days, but at 6 days and higher, I don't see it.
It looks like a valid bug, and I didn't see any record of it in the Kibana Github, so I filed a bug report for it: [Timelion] X-Axis shows times but not dates in the X-Axis for certain time picker ranges · Issue #13065 · elastic/kibana · GitHub