The conquest of Italy started off well in 536 with the quick taking over of Sicily and then Naples after some resistance. Once Belisarius reached Rome however things slowed down. He entered the city unopposed but there were significant challenges in holding they city. Food first of all there was the issue of feeding the poplulation and secondly the wall circuit of Rome was enormous and the city itself had no gates. There was a one year siege of the city (537-538) which was successfully repelled.

Belisarius eventually conquered most of Italy by 540 including Ravenna the capital.

So the initial conquest was only 4 years long but holding the gains would prove difficult and wars would last two decades. See this wikipedia article on the Gothic wars for more in depth information:(https://en.wikipedia.org/wiki/Gothic_War_(535%E2%80%93554)#Fall_of_Sicily_and_Dalmatia_to_the_Byzantines)

Compared to the conquest of Africa where the Vandals had only two fortified cities (Hippo and Carthage), the Goths left the walls of the Italian cities intact and thus had more strongholds to retreat to and retaliate from.

The Goths also had allies such as Franks and Persians who would distract the empire and force resources elsewhere.

Lastly there is the problem of Justinian not trusting his generals' loyalties and splitting up armies in between them. The generals did not always cooperate either and at one point many just holed up in their own cities with their treasure and individually knocked out. There is a fun little reference to this in computer science known as the byzantine general problem

Luckily we have great sources primary on this era thanks to Procopius's Wars and Secret History and his being present with the armies.

I would put most of the blame on Belisarius. Justinian's decree would have given North Italy (Po Valley?) to the Goths, which would have acted as a buffer state. The Empire would have acquired the rest of Italy at a point when the costs of operations was light. But Belisarius' disobedience of Justinian and treachery to the Goths galvanised resistance. Collins also point out that it's also possible Belisarius was going to accept the Western Emperorship but could not get support from his army, half of the officer of which did not trust him.* Procopius blames Justinian's jealousy of course, but considering a renew Persian War was looming and Belisarius was ordered to take over the Persian front and reinforce it with his Gothic captives, jealousy or not it was an incredibly sound decision.

The Goths elected Baduila (Procopius calls him Totila) a far more competent leader than the previous two Belisarius faced (the first one, Theodehad, it seems had be wholly incompetent), who went on the offensive with the empire distracted in the East. Belisarius returned to Italy later, but without adequate forces or the divergent campaigns of his first conquest due to the eastern needs, empire suffering from plague and economic down turn, and/or Justinian's jealousy and not trusting Belisarius anymore.

*Early Medieval Europe by Roger Collins.