I guess in order to answer that question properly, one has to count in a few factors:
Firstly, the Hellenistic States were quite volatile: As soon as you lost a war, there were many parties (usurpators, regional governors with aspirations to build their own state, the other Hellenistic kings) that were armed and ready to completely tear your empire into pieces. Especially the Seleucid Empire was vulnerable to "centrifugal" tendencies and had shrunk to about half its size before Antiochos III came into power. If Antiochos had decided to extend the war on Rome, he would have risked that his eastern provinces such as Bactria and Parthia would defect, while in the best case win highly disputed land in Asia minor. On the other hand, Ptolemy, whom he had just defeated at Raphia 195 proposed to enter into the war together with Rome, an offer that the Senate refused, but if the war would have went on for much longer, they probably would have either accepted his offer or Ptolemy would have waged war against Antiochos on his own seeing the success of Antiochos crumble. So, anything else than peace would eventually have caused even more damage to the Seleucid empire.
Secondly as much of a recruiting area as the Seleucid Empire may seem, it was actually quite uncommon for Hellenistic kings to recruit the non-Greek population for their wars. The core of the troops (the so-called phalanx and the argyraspides) of the Seleucid army was recruited from some 45 military colonies that the Seleucids had scattered all over their empire. The strength of that group is estimated to be 44.000 hoplits. App. Syr. 36 counts 50.000 losses on Antiochos site, so even if we say only half of those losses (the lowest possible estimation) were core-units, that would leave us with more than the half of the military strenghth of that group wiped out. To recruit anew Antiochos would have to wait until the population of his settlements regrew. Other possibilities of recruitment were not available: Training the oriental population would have been an enormous task that would be carried out at the risk of uprisings. The Greek Mainland on the other hand, was off limits for Antiochos in terms of recruiting: He had started the Romano-Syrian War by transporting troops across the Ionian Sea in hope to find allies against Rome in the Greek mainland but was soon to find out nobody actually wanted to side with him. The Rhodians, who effectively controlled the sea at that time, had sided with the Romans so the Mediterranean was blocked for the recruitment of Greek mercenaries of the Islands and the mainland.
Thirdly it didn't seem like he could win back the city-states of Asia Minor as easily, as he had overtaken them in the first place: Until the coming of Rome the Greek world had put on a complicated diplomatic facade of freedom. The Greek city-states were granted full freedom from their sovereign, as long as they stood in line and didn't defect to another Hellenistic king. However, the sovereign had his means to reach out to those city-states: Often when a king took over a city, he would install a party of people favourable to him. Additionally, the new king was deified and got a cult in the city. And it is pretty hard to press your motion against the will of a god. When Antiochos made his grand campaign through Asia Minor at the eve of 200, he used the same tools his predecessors had used to grant that his newly acquired city-states would stay in line: He installed cults for himself and exchanged the leader boards of the cities. But this time it would be different: The people had tasted what real freedom was like. When Rome had advanced into the Eastern Mediterranean, they had little ambition to control the land in a strict way (A thing that should lead ultimately to the downfall of the Roman Republic). Instead, they just send military aid, if necessary, and otherwise let the Greeks deal with their own regards. Having perceived that style of rulership, the Greeks of Asia Minor previously subdued by Antiochos began to side with Rome in their own way: Cults for Roma (an interesting turn of events: they couldn't single out a "Roman ruler" so they would just worship the city as a whole) began to pop up in Cyzicus and other Greek city-states and this behaviour would intensify during the war. Antiochos had little chance of winning those city-states back into the old way of "freedom".
Lastly and maybe most importantly, he fought an uphill battle. Antiochos had waged war against Rome hoping the picture of his being the "saviour of Greece against the barbarian threat" would spread across mainland Greece and he would have enough allies to exclude the Romans off the Eastern Mediterranean. He had made a deal with an Antiochos-favourable Aitolian party, who managed to conquer Demetrias as haven for Antiochos. But when he reached the Greek mainland in late fall 192, the tables in Aitolia had turned against him and he lacked even a single ally in Greece. But his rapid expansion and imperial policy had made many of his rivals, such as Philip V, whom he had effectively alienated by his advances into Asia Minor, Ptolemy V and the Rhodians, the Attalid kingdom as well as all of the Greek mainland side with Rome.
Traditionally scholars see the Battle of Magnesia as the starting point of the downfall of the Seleucid empire: The Hellenistic kingdoms were effectively fed by the Mediterranean region and the loss of control over his ties with the eastern Mediterranean (at least the parts in Asia Minor) started the decline of the Seleucids. More recently scholars like Susan Sherwin-White and Amelie Kuhrt argued that Greece was in no way that important to the Seleucids and that their empire only started to crumble as the eastern provinces, Bactria and Parthia, finally went their own ways. Still, we shouldn't forget that the Seleucid empire despite its enormous size in the times of Antiochos was no more a "superpower" overshadowing the Mediterranean as were the Ptolemaic and Antigonid kingdom.
Sources:
Generally:
For the Seleucid Army:
For the cities in Asia Minor:
ยท John Ma: Antiochos III and the cities of Western Asia Minor, Oxford 1999.