This isn't my area so I won't be surprised if a better answer comes along, but I suspect that its remoteness was more of a help than a hindrance when it came to protection.

Firstly, it was far away from the normal trade routes along the Euphrates, surrounded by desert (Ball 74), however it was still a trade nexus and to some extent this was apparently a product of military power and coercion, as Palmyra was one of the only clients of Rome in the east with a permanent army (74). Indeed, when the Palmyrenes and friends rebelled under Zenonbia they are alleged to have attacked the Romans c. 270 AD with 70,000 troops (80, probably exaggerated). Like most cities in the militarised east, it must have been quite well fortified, and when the Romans attacked it after Zenobia's rebellion in AD 273, it took some effort to take (80).

Its isolation from the population and economic centres of the Euphrates corridor was also helpful in that Roman-Persian confrontations tended to occur in northern Mesopotamia, where all the juicy targets and where armies could be easily sustained (Lee 712). Just as the Persians tended to attack in the general direction of Antioch, the Romans tended to attack in the general direction of Ctesiphon. This put Palmyra, an economic powerhouse that no doubt played both sides to its advantage where it could (74), way out of the line of fire.

Ironically, that Roman soldier was probably wondering why the Persians never attacked it, since Palmyra would have been far too well defended for any Arab tribes or bandits to take. And yet it was the Romans who eventually trashed the place. While the emperor Aurelian gave them a pass after he crushed Zenobia, the Palmyrenes (who hadn't read their history books about Jerusalem and the Jews), rose again a few years later. Aurelian came back, and this time he handed the city over to his troops. Palmyra was razed, its artifacts looted, and its populated all but destroyed.

Sources:

Warwick Ball, Rome in the East: The Transformation of an Empire, Routledge, 2000. Available on google books! https://books.google.com.au/books?id=73-JAgAAQBAJ&pg=PA77&redir_esc=y#v=onepage&q&f=false

A.D. Lee, Roman Warfare with Sasanian Persia, from the Cambridge History of Greek and Roman Warfare, 2007, 708-725.