Despite the frequent turnover and turmoil in leadership, the Empire did survive.
I think this relative stability can attributed to Intact institutions (extended family, a patronage system, religious organizations, etc) and a well-entrenched bureaucracy.
In Italy there have been 36 (and counting) Prime Ministers since 1946. Despite these frequent changes of government, daily Italian life is barely affected by these transitions. Similar to Ancient Rome, people merely meet the challenges of life, supported by their local family, relationships, religious affiliations, etc.
This might explain why distant communities would continue living a Roman lifestyle long after the Empire and the city of Rome “fell.”