It's something I always wondered. When things got bad, why did the Romans in the West not simply abandon their frontier and hold Italy? Why did they allow Rome and the Italian heartland to be raided over and over while trying to hold Africa and Gaul/Germania? It seems logical that when you see you're overextended to simply retreat within a smaller area even at the expense of your empire.
I suppose the last question I have is what happened to the Romans manpower over time that prevented them from responding to the tribes?
For example, in the Punic Wars, Rome lost tens of thousands of men, but could field more and keep up the fight, all mainly from Italy. Was the economic decline of the West over the centuries really so bad that they simply couldn't field more men no matter how bad the crisis?
They effectively did. The end of the Western Roman Empire, left a gothic controlled, but more or less Roman rump state in Italy, that lasted until it was conquered and dismembered by the Eastern Roman Empire and the Lombards a lost a century later.
When Flavius Odoace (a Goth) deposed the Emperor Romulus Augustus in 476. The act which signifies the end of the Western Roman Empire. He did so in order to become "King" of Italy. The Ostrogothic Kingdom of Italy lasted for a little less than 100 years, when it was invaded and dismantled by the Eastern Roman Empire under Justinian. The ERE one again lost control of the hinterland of Italy to the Lombards, in part due to over extension and plaque.
I want to make a general response to the basic question/assumption:
The Romans did indeed pull out several times over the course of their long existance. They were not stupid. In Britain, they retreated from the Antonine Wall in about 162 AD; they eventually more or less left Britain about 410 AD. There was some sort of gradual process; the last I time I read about it they were not too sure of the details and exactly how it came about. But most likely left because of general unrest/invasions in the empire.
The Romans did not stay long in Parthia (NE part of Iran); they left at some point but I cannot recollect the actual dates.
The Romans had to pull out of Germany in light of the defeat of Armius, about 9 AD. Recent research puts this battle further north than prevoiusly believed. (I think near Koln) but in any event the research of just a few years ago seems to have been part of a general pull out that was taking place from certain German cities. THis extent of Roman empire into Germany is often not shown on maps, but it also represents a pull out for sure.
THe emperor Diocletian changed the capital from Rome to Milan in 286 AD. They later made Ravenna the capital about 402 AD. Most historians agree partly for defensive purposes owing to the marshes. Leaving your capital has to be considered a pull back.
The Romans may have pulled out of Noricum (Austria/Slovenia/e.Bavaria) by the end of the 4th cent. The knowledge on this area seems to be spotty. The border along the Danube is hard to figure on the history. It may have been overrun by the barbarians, and the Romans may have decided to defend it.
You may also want to research the confused history of Dacia, where the Romans pulled out several times. Notably in 275 AD and 336 AD but there were other times as well.
So the basic question assumes that Romans did not pull out. The Romans were NOT stupid they pulled out at certain times, and much of it is not clear. The barbarian invasions were part of giant cataclysm involving, economics, society, biology etc. and even the Romans could not avoid it.
This is a general answer, I dont have time for references, but will come back later if you wish to continue.