Yes but why exactly? The republic fought at all fronts simultaneously and won... Why wasn't the principate, better organized than the republic, able to stop the invaders at the borders?
Fact is, the roman empire of the principate was not able to defend the empire, when attacked at many fronts at once. Not militarily, not politically, not economically and also their society was not appropriate to do so.
Defensive wars were not the sort the Republic ever truly excelled in, and the fighting they did in all directions was also under the direction of various generals who, in their corner of the empire, held de-facto absolute authority. You can't get away with that sort of thing when those very men who should holding your territory want your position, this forces you to be in all places at once trying to hold together a realm with string and tax money because you're too scared to lighten your workload.
Why their society isn't appropriate, is because of the inability for any one man to command the unquestioned loyalty of his subordinates in the majority of instances, this along with the lack of will in the apparatus to deal with foreign threats simultaneously while maintaining itself in a stable fashion.
The ways the Empire dealt with excursions was to siphon away resources from other slightly less volatile hotspots and send troops in a new direction, in the Crisis the split in Gaul more or less managed to hold up its part of the fence while a separate regime was allowed to hold down its part. The division of authority being the only way for this sort of defense to be successful. However it's already been stated why division of authority is very much a bad idea, and in the crisis it was also demonstrated why that was a bad idea (generals killing each other for the position of Imperator).
Now that I've said that, When did the Republic have to hold an invasion from the north, attacks on any overseas territory as well as the south. There has been no time that I can recall where the borders of the republic were just continually punctured by foreign expeditions? Also, better organization doesn't necessarily prepare the empire for the sorts of threats it had to weather.