Most Italians leave the cities in August and head for the beach primarily and some head for the cooler mountains. Infact I read in CorriereDS a few days ago that the major cities will be half empty this year (as in past years). In Rome in August all you can seem to find are tourists so yes many things are closed.

If you only have two days though there will be enough open for you to occupy yourself. Pick up an eyewitness guide before you go.