You would have to pick a specific time and place which you see as the quintessence of romanitas before anyone could give you a straight answer. Every single citizen of the territory controlled by Rome from 700 BCE into the 9th century and those in territory controlled by Byzantium until 1453 could and would consider themselves "Romans".

So, that's a lot of different things which are recognizably Roman, some of which Italy never was.

Native Italian speakers stopped being able to understand spoken Latin without study some time after 1200, if that is any help.

/u/telkanuru's comment is especially relevant when you consider that what we consider Roman (pagan high imperial) is not what a lot of medieval europeans considered roman (christian late imperial).

A lot of the medieval renaissances (like the Carolingian and the Macedonian) had this explicitly in mind (the idea of the christian roman empire) as to what they were "renewing". It's only once the Italian 15th century renaissance kicked off that people started viewing Roman the pagan way we do now.