The Roman Empire was, after various configurations and reunification, definitely separated into two distinct states, western and eastern, by the late IVth century. While the Eastern Roman Empire beneficed from a strong position, as the Persians relieved the pressure on eastern borders having to deal with their own "Barbarians", and as the eastern provinces were mostly untouched by the damages caused by raids and civil wars of the IVth century (being protected from European Barbarians by the Roman naval dominance) and even underwent an economical and demographic growth in this period; the Western Roman Empire was in a more precarious situation.
Western provinces were more vulnerable to a break of the limes, and when attacks resumed in the early Vth century in Pannonia and in Gaul in roughly the same time, it proved too much to be handled especially as it was doubled with a political crisis. Without going in details, Ravenna lost access and control of a significant part of its provinces at the benefit of Barbarian autonomous armies which formed states-in-being : the loss of the rich African province was particularly felt as it represented an decisive part of fiscal revenues.
Italian senatorial elites eventually choose in the mid-Vth century to focus on protecting Italy at the expense of a costly strategy of provincial reconquest, which led the rump empire to be essentially an Italian state, leaving the rest of the provinces prey to various warlords (either Barbarian or Romans) whom Ravenna, dominated by Ricimer, a powerful semi-Barbarian leader, searched to ally or to fight against depending on the situation. This "patrician" Italy (due to the name of the de facto strong men of the state) survived the formal end of the western empire when Odoacer deposed Romulus, leading a Barbarian army (as every commander in the era, either Roman or Barbarian) : there wasn't a proper imperial army at this point, only the semi-private armies of petty-kings and generals, and Odoacer (a former protegé of Ricimer) simply had access to more troops and more connections than Orestes.
Constantinople didn't intervened, seeing most emperors in Ravenna as essentially illegitimate authorities since Valentinian III, and not having troops or funds to spare to continuously keep the rump western state on life support trough proxies (which were generally distrusted by Italian elites and Barbarian alike). Odoacer having meddled in eastern politics however, Constantinople tasked Theodoric with taking Italy back into imperial authority; the various Barbarian kingdoms being seen as autonomous part of an Empire whom emperors in Constantinople were the sole rulers. It's not that Romans recovered after being "bested", it's that we're not talking of the same Romans.
Gathering an army whom "Gothicity" can be debated, Theodoric thus took over the peninsula with Roma support and made his best to restore the late imperial state in Italy, at his benefit (and as Constantinople sent him the imperial insignias in 497, having a general claim to be sort of a vice-king for the whole former western provinces).
When Romans underwent the conquest of Italy in the VIth century, mislead by a quick defeat of Vandals (although stabilizing Africa would cost them more time and resources) and thinking it would be the same in Italy, they were backed by the resources of an Eastern Empire mostly relieved from Persian pressure for a time; not a rump empire limited to Italy and led by competing generals. While Belisarius was sent with only part of the army sent in Africa, and in spite of an easy enough initial campaign, he was regularly supplied with more men (in addition to troops sent in Dalmatia) and even that proved not be enough to really defeat Goths : saying that Italy was conquered with a "much smaller" force would be misleading.
- The Fall of Rome; Peter Heather; 2005
- Rome Resurgent: War and Empire in the Age of Justinian; Peter Heater; 2018
- Late Roman Warlords; Penny McGeorge; 2003
- Theodoric and the Roman Imperial Restoration; Jonathan J. Arnold; 2014