The collapse of the Roman Empire during the third century began with Maximinius Thrax who decided that raising taxes would not be too upsetting to the rest of the Empire. As he levied the taxes to support his war with the Dacians and Sarmatans, rebellions began in Africa and swept across the Empire. This by itself was not the reason the near collapse, but it opened the door for Rome to continue down the slippery slope they started. After Thrax’s assassination, Gordian III stepped up and met a similar fate. During this roller-coaster ride of emperors coming on and off the throne, wars were increasing from every area of the Empire with Persia and other barbarians attacking. The Augustian army structure was not up to handling multiple attacks at once from different areas of the Empire. The army found itself literally running from one end of the Empire to the other. The plague sweeping across the land did not help in keeping the Empire strong.
Mutinies became common as the wars began to deplete the economy and war was erupting from within Rome itself. The Roman Empire was beginning to collapse because it had not adjusted its military to its new monstrous size which allowed barbarians to inflict damage on the Empire by raiding various regions. With no emperor staying long enough on the throne to do anything and all emperors fixated on protecting their lives and killing off any potential usurpers, it was almost inevitable for Rome to collapse.
It was Gallienus that actually saved the Empire. He took over a land that was in chaos and began reorganizing the army so that it could better meet the defensive needs. Gallienus revived the culture in the arts as well as calming the internal turmoil of the Empire. After his own assassination, his successors took up where he left off and began to stabilize the downward spiral of the Empire. Though his name is not as well known as later emperors that were successful due to his work like Constantine, he was the one to pull the Empire up and get it rebuilding its foundation.
Marcel Le Glay, Jean-Louis Voisin, and Yann Le Bohec. A History of Rome. (Malden: Blackwell, 2009).