A bit of background: Petra was founded by the Nabataeans, Arab nomads that controlled the drylands between the Levant and Arabia and the lucrative caravan routes that passed through them. Petra was well placed to be the hub of their trading network, but it was a difficult place to actually live because, well, it was in the middle of the desert. The city relied on an sophisticated hydro-engineering to survive. The only water it got came in the form of occasional seasonal flash floods, so the Nabataeans built an elaborate system of dams, aqueducts and systems to collect as much of this water as possible and divert it to terraced farms to grow food.

The labour and resources needed to construct and maintain that system was justified by the immense wealth Petra generated through its control of caravan routes, and as long as that was the case the city thrived. But the commercial importance of the city began to wane as early as the 1st century CE. Petra's bread and butter was the incense trade between Arabia and the Mediterranean, but as the Roman Empire expanded into the Levant it fostered new routes that circumvented the city: bringing incense across the Red Sea to Egypt by ship, or along an eastern caravan route that went through the Roman city of Palmyra in Syria. In response, the Nabataeans shifted their focus to Bosra, a rival city situated on the route between Arabia and Palmyra.

This wasn't a death knell for Petra by any means, it still controlled a lot of trade and adapted by increasing the amount of agricultural and industrial taking place in the city itself, but it was no longer the sole political or commercial hub of the Nabataeans' trading network. The real decline in its fortunes started in 106, when the Nabataean kingdom was annexed by the Romans. Petra became the capital of the province of Arabia Petraea, but it was neglected. Few new buildings were added to the city in the Roman period and since it no longer had any independent political clout trade continued to slip away from the city in favour of Palmyra. By the end of the 3rd century it was falling into disrepair, and in 363 a major earthquake destroyed much of the city and its critical water management infrastructure. Most of the damage was never repaired making it clear that by this point the city was in steep decline. It limped on for several more centuries, but several more earthquakes damaged the city and the population slowly bled away to smaller towns and villages, and it was finally abandoned when it was conquered by the Arabs in 663.

Sources:

• Fiema, Z. T. 2003. Roman Petra (A.D. 106–363): A Neglected Subject. Zeitschrift des Deutschen Palästina-Vereins, pp. 38-58.
• Kouki, P. 2009. Archaeological Evidence of Land Tenure in the Petra Region, Jordan: Nabataean-Early Roman to Late Byzantine. J. of Mediterranean Archaeology 22(1), pp. 29-56.
• Wenning, R. 2007. The Nabataeans in History. The World of the Nabataeans, pp. 25-44.

Follow up question, was this decline related to the broader climate change in the near east at the time?