At least 3 of my history teachers have quarreled with the subject when asked about it. Was the reconquest of the West squandered by his worry of Belisarius taking power or did it come from a more reasonable understanding of the current climate within the empire, that being one of serious disease and near constant war with the Sassan Persians. I am very curious if this can be objectively proven one way or another.
I've written a few times before about what Procopius actually recorded about the war in Italy after Belisarius first took Rome in 536. You can read about that here, here, and here. While it could be argued that Procopius' Secret History is a "more accurate" portrayal of Justinian and Belisarius (see discussions on the Secret History here by /u/shlin28 and /u/bitparity), the fact remains that in the Gothic Wars, the actual record about the fighting in Italy, Justinian seem fairly supportive of Belisarius, sending him multiple reinforcement throughout the war, and only recalling him both times due to needing him for war with Persia, and the Gothic Wars also records various problems with and mistakes made by the Roman commanders in Italy, including Belisarius.
Having said that, I think you might have mixed up the history. Although it was through tremendous effort, the wars ended with the successful reconquest of Italy. In that regards Justinian did not fail.