There were TWO major plans subsumed under Operation Barbarossa. The plan for 1942 was called Fall Blau (Case Blue) and called for an emphasis on attacking the Caucasus, per the question. The basic reason it was abandoned was that it was the "backup" plan. The original (1941) objectives of Barbarossa was the so-called A-A or Archangel-Astrakan line. Elements of the earlier A-A plan eventually got mixed up in the 1942 Fall Blau.
After the initial failure to capture Moscow in 1941 (and the unsuccessful Soviet counterattacks around Kharkov in May, 1942), Hitler decided to shift the emphasis of the offensive south, toward the Caucasus. But once the Germans began enjoying successes, he diluted the Fall Blau plan by reinstating elemenets of the A-A plan.
Early In July, Sevastopol on the Black Sea finally surrendered to General von Manstein's 11th Army after a 9 month siege punctuated by unsuccessful Soviet counterattacks from the Kerch Strait. Hitler decided to move both Manstein and the 11th Army north to try to take Leningrad, thereby a allowing a resumption of the northern prong of the attack toward Archangel. The earlier planning for Fall Blau had the 11th Army joining the attack on the Caucasus.
The original plan for Fall Blau had German detachments going up to, but not into, the cities of Vornezeh on the Don, and Stalingrad on the Volga. The plan was to remain on the defensive outside these cities with (eastern) flank guards. and have a south facing thrust to the Caucasus.
The unexpected capture of Voronezh and 6th Army's rapid progress along the Don lulled Hitler into thinking that Stalingrad (the namesake city of the Soviet dictator) could also be captured. So instead of keeping Paulus' 6th Army on the defensive, it was posted on the offensive, with Herman Hoth's 4th Army (originally slated for the Caucasus) in support of the attack on Stalingrad. The diversion of this and the 11th Army cut the strength of the Caucasus attack force (two armies) by about half.
One lure of Stalingrad was that it was on the Volga River, the intended eastern boundary of the A-A line. If the city had been captured in September, the German could have proceeded down-river to capture Astrakhan, establishing the southern portion of the A-A line. Then the plan for 1943 might be to advance up the Volga behind Moscow (in the south), while capturing Leningrad and Archangel the same year, followed by a gigantic pincers encirclement of Moscow in 1944.
But rationally, Hitler should have gone for the (almost) "sure thing" in the Caucasus, instead of gambling on knockout blows at Stalingrad and Leningrad that failed. But that's another story.