First off the Persia that Rome was facing in the third century was not the same as the one it faced in the second. The Parthian Empire that defeated the legions of Crassus collapsed in the early third century and was replaced by a much more bellicose Sassanian Empire. Under Ardashir the Sassanids made frequent incursions into Roman territory, and his son Sharpur was able to sack Antioch and capture the Roman Emperor Valerian.

This period of Persian resurgence coincided with greatly increased pressure on the Rhine and Danube frontiers. Tribes that the Romans used to be able to divide and co-opt using clever diplomacy were increasingly united in coalitions that were less inclined to negotiate.

This combination left emperors of the period with two choices: try to meet all threats personally and inevitably fail or delegate responsibility to their generals and face revolt. This created something of a 'perfect storm' for the Romans and a perfect opportunity for the Persians who expanded their empire at Rome's expense.

Another related question was that in David Potter's book on constantine he says that in the 3rd century leather armour was becoming favoured over metal, this seems odd where does this claim come from?