You'll need access to the scripts of your dashboard for this (i.e. this should be a dashboard you can edit), and there are several possibilities.
The easiest one should be to set a fixed opacity for those elements. If you haven't already, apply a stylesheet (add stylesheet="custom_style.css" to your dashboard or form tag in XML and place custom_style.css in your apps appserver/static folder) and add
.view-results {
opacity: 1 !important;
}
to it. This prevents the events (focusing and de-focusing the panel) from hiding the elements. This would apply to all buttons in the footer and to all footers; if you want only the export button to stay, you'll have to make a more precise selection.
A possibly nicer way would be to disable the event action upon focus (you can see the method that is called on those events when you use your browser to inspect the panel footer).
