I was watching the awesome Extra Credits season about Justinian and Theodora, how he recaptured North Africa, Sicily, Italy and even a bit of Spain. Unfortunately, the series ended after the defeat of the Ostrogothic army after it wanted to recapture Rome.
It was lost again.
In Italy the war with the Ostrogoths lasted for decades and devastated the country. Some historians hold this war to be the true end of antiquity. As Goldsworthy puts it, it "probably destroyed many aspects of Roman culture and society that had survived the collapse of the Western Empire."
Although the Byzantines eventually defeated the Ostrogoths and took control of the whole of Italy, the Lombards (Or Longobards, i.e. Longbeards. Another German tribe) invaded Italy very soon after Justinian's death, and took over most of the interior. The Byzantines held on to coastal cities and Sicily, and over the centuries afterwards would sometimes regain parts of Italy, but they never got anywhere close to achieving Justinian's territorial ambitions. They fought over it as late as the reign of Manuel Komnenos, who tried to regain control over the southern ports there in the 12th century.
The Spanish possessions were contested by the Visigoths, and though the Byzantines held on for some decades, and even made some temporary gains by exploiting Visigothic dynastic conflict, they lost all their mainland possessions in the 7th century even before the Muslims invaded. (They held on to the Balearic islands for a bit longer.)
Africa remained a Roman possession for several generations, until it fell to the Arab invasion along with Egypt and Syria later in the 7th century.
The bubonic plague that devastated the empire shortly after the start of the Ostrogothic wars likely had something to do with the empire's inability to hold on to its conquests, but Justinian's projects had also been opportunistic and ended up opening up several new fronts in an empire already struggling to defend its existing possessions from attack. Hardly anybody considers the loss of the new conquests surprising.