Salesforce Email button not appearing on Activity Component

Disappearing Email button on Page Layout

Safe Harbor 😉 : Every once in a while we come across a certain unexplained phenomenon in Salesforce configuration. The only fun outcome of such items (after getting resolved) are the facial expressions of technical architecture pundits. By the way these one off phenomena often seem to disappear mysteriously in the next couple releases of Salesforce as well (kudos to SF Dev team as always). 

I recently came across one such craziness .. 

The email button wouldn't appear on a sandbox on the Activity component. Yep, it should appear by default typically .. but it wouldn't ..

If you notice that after adding & saving the Email button on the page layout (Lightning Experience Buttons), when you refresh the page layout the Email button doesn't get added, it disappears .. then you are at the right resolution path below.

Resolution:

Setup > Administration > Email > Deliverability > Access Level needs to be All email.

Check whether this resolves the problem .. if not .. then proceed to 

Setup > Administration > Email > Enhanced Email > (If enabled, Disable it)

This should do it.

Now go back to Enhanced Email and Enable it. 

References:

Salesforce Help Article