The Romans preserved and restored old and damaged buildings all the time, as well as completely rebuilding structures that had been totally destroyed. It was a major part of the monumental building projects that made up such a crucial part of the urban economy, as well as preserving the dignitas of the restorers. Some of the most famous buildings in the city were rebuilt or restored: the Pantheon (built by Agrippa under Augustus but restored by Hadrian after it caught fire), the Curia Julia (a rebuilding of the Curia Hostilia or Curia Cornelia, which was destroyed by Clodius' partisans), what's left of the Temple of Concord (rededicated and restored by Tiberius on the rebuilt temple constructed by Opimius), the Basilica Julia (rebuilt after a fire in 12 AD and again by Diocletian after another fire), the Temple of Jupiter Optimus Maximus (restored and added to extensively over the centuries), the Temple of Castor (rebuilt by Tiberius after a fire), the Temple of Vesta (destroyed and rebuilt repeatedly), etc. I could go on for some time. You'll note, and likely object, that most of these buildings saw significant renovation or even complete redesign during their restorations or reconstruction. To the mind of the Roman aristocrat, ever-competitive and eager to demonstrate the preeminence of his own dignitas, a restoration project was not only the reconstruction of a damaged or destroyed structure, but a new monumental building project in its own right. Particularly during the Principate (but also very much under the Republic), when emperors strove to indicate their superiority over their predecessors and aristocrats like Agrippa maintained their own public image with what few remaining means they had available to them such a project was a major draw. Septimius Severus, for example, restored Hadrian's restoration of the Pantheon alongside Caracalla, and added an inscription mentioning that he had restored the structure, even though unlike Hadrian he had not made any significant changes. This, on a relatively minor reconstruction project! That the monumental structures (and even non-monumental structures of great importance) had to be periodically renewed and preserved was obviously foremost in the Roman mind. These were ancient structures, often religious in nature, preservations of the all-important mos maiorum--indeed, given the obsession in Latin literature with the past and the importance of the mos maiorum I struggle to see how the impression that the Romans cared little about the past could possibly arise. So important was the preservation of buildings exemplifying the mos maiorum that the Romans religiously preserved what was traditionally the oldest building at Rome, the casa Romulus (hut of Romulus), on the Palatine--the post holes of what is often considered to be the site are still extant and visible today.