I think Rome’s success abroad Italy had more to do with the actual army model rather than lack of motivation by her enemies. Of course, the huge numbers at Rome’s disposal, and her military ethos, tremendously helped, but if subsequent wars were as brief as they were, I’d say that owes a lot both to the inefficiency of the phalanx against the Roman army and the huge amount of mercenaries employed by Hellenistic armies. Antiochus III was certainly determined to establish a foothold in Europe, and had the resources to do so, but his attempts were met right away with defeat, and other defeats soon followed. No wonder he lost all motivation after that.
Hmmm... Antiochus was determined, but he was not prepared to lose his kingdom. The Romans were prepared to throw army after army at him until he accepted their conditions. He probably knew that (as Hannibal had just gone through exactly that), and while his realm was equal if not superior to the Republic in overall wealth and population, he could not even remotely match the Romans in military numbers. As soon as the field engagements went the way of the Romans, he knew that throwing the sponge was in his best interest. That's what I mean for "not determined".
It is possible for the phalanx to defeat a legion (Pyrrhus did that after all). But in the end, a lost battle would have been almost irrelevant to the Romans. They'd send other legions, and the overall superiority of their military would have told through sheer obstinacy and numbers if nothing else. Antiochus could not afford to lose armies at anywhere near the same rate. Rome would have a breaking point somewhere too (and they were arguably fairly close to it after Cannae) but just look at the grievous losses they kept taking in Spain in the second century for, what, three generations? Now, well, those were determined foes. They defeated legions repeatedly with forces far less structured than a phalanx. They still lost, badly. And the Roman vengeance on the Arevaci and the Lusitanians was terrible.