How to "keep in touch" with a potential advisor?
When a member of academic staff says "Keep in touch" to a leaving student or researcher it often means "Keep me informed with major events in your career or family". Yes, it probably has the expectation of an email, but not too regularly.

They are probably interested in where you might be working when you have left and want to be informed of how to contact you when your contact details change. I sometimes get an email from students who have left 5, 10, 15, 20 years in the past. They tell me "I now work for XYZ corp as VP of ABC, how are things back at the University?", or "My child is applying to study with you, is Prof. PQR still there?". It is all good to know.

There are other times&dagger; I might used the phrase in an email with someone. If I was telling them that I was the wrong person to contact about an issue, or that this is the wrong time to discuss an issue; in other words, if I was refusing an answer, I might add "Let's stay in touch" to indicate I was not refusing all contact for all time. Sometimes students mistake a refusal to answer with an end to all communication. For example, at this precise moment in time I know all graduates results but could not answer any questions about progression to a Phd programme as that might imply what the grades may be&Dagger;. In that case it would mean, "At the appropriate time you will have the information you need.." or similar.



&dagger;This paragraph added based  on further details in the comments.
&Dagger;Result discussions are currently embargoed till transcripts are officially released.