Historic buildings are old buildings which cannot be compared with new construction but its important to consider sustainability of existing buildings not only in design for new buildings.
It really depends on how you defines sustainability.
You can argue that having survived - to be old or historic - makes them sustainable to a certain degree (people like them, don't want to demolish them, they want to upgrade them and keep using them)
If you look at it from an energy perspective - it depends. Some older buildings have better environmental qualities (specially if they were built using local knowledge and practices). Some others (like "modern" buildings from the 60s to 90s in many cities) are problematic environmentally and would require retrofitting (new envelopes, new HVAC systems, or even removing old materials such as asbestos, etc....)
Historic buildings in perspective of archaeology are "living" bodies, not only an inorganic envelopes. They interact with current human societies activelly. Current stand of any historic building reflect recent motion in human society. They are memories and memories could be reconstructed in current style.
Dear Jaromír Beneš I agree with your reflection; however, it is necessary to make a critical reading of what exists to intervene on it through the architectural project
Dear Fabián Andrés Llano I absolutelly agree. Sustainability shoud be then regarded as keeping of original material expression and soul of the building in its new role.