That was fine for a few centuries, until external enemies re-emerged, and then it really fell apart.
The wealthy of Rome were not willing to pay for all of this, so the practice was for generals to pay their soldiers out of taxes and loot. Thus the legions became loyal to their generals instead of to the Republic, which essentially made them warlords. There were plenty of places left to conquer - Augustus would somewhat famously and disastrously try to conquer Germania east of the Rhine, Egypt was assimilated after Pompey's defeat, etc.
Interestingly, that disasterous campaign you mentioned by Augustus to try to conquer up to the Rhine was done exactly to address the difficulty of defending Rome's extended borders. He felt that it was important for the empire to achieve its natural borders, just the same as France sought to do after the revolution.
However, even had those natural borders been secured, it would have done nothing to address the internecine strife that was was instrumental to the decline and final collapse of the western empire. It is necessary to look at a combination of both internal and external pressures to explain what happened.