Although many hailed Trotsky as the architect of the Red Army in the Civil War- including the man himself- his involvement within the peacetime military did not significantly strengthen his political hand in the post-Lenin period. The political power of the Red Army was quite limited within the early years of the Soviet Union.
Despite state propaganda that celebrated the Red Army as one of the vanguards of Soviet socialism, the immediate postwar years were lean times for the Soviet military. Budget cuts and demobilization were needed to return the country to something of a sane state after the chaos and economic dislocation of war, revolution, and civil war. Trotsky himself was in an unenviable position in the postwar period as he often butted heads with the various military specialists like Frunze and Vorishilov over the structure and doctrine of the peacetime military. Counter-intuitively, Trotsky often derided the specialists' cult of the offensive and argued that the Red Army should be used as a shield of the Soviet state, not as a tool for revolutionary adventures abroad. Frunze and Vorishilov tended to be much more Trotskyite in their approach to doctrine and grand strategy. Part of this was political posturing, but there was an attempt by these specialists to square military strategy with Marxist-Leninist ideas. But the leadership of the Red Army was in general not comfortable with Trotsky and often used these acrimonious debates in the Lenin period to oust Trotsky from his position in the Red Army. Trotsky's partisanship for a national militia over a professional force also did not win him any fans among military professionals.
Trotsky's close association with the military was also a liability for him with other Bolsheviks. The historical model of both the French Revolution and the Brumaire coups of both Napoleons made many Bolsheviks leery of potential "Bonapartists" among their ranks. The idea that the military could be used as a tool to stop or reverse the revolution was one of the staples of Marxist thought in this period. After all, the most loyal institution of the tsarist state had been the army. Added to this, many leading Bolsheviks did not trust the army. The exigencies of the Civil War had meant that the bolsheviks had to rely upon a number of men whose experience in the old imperial army trumped their lack of revolutionary credentials. Although some of the post-Civil War military thinkers often framed their doctrine in revolutionary terms, many Bolsheviks simply did not trust these specialists. Both the OGPU and its successor the NKVD spent an inordinate amount of time investigating the Red Army for potential treason, wreckers, and counter-revolutionaries. This later climaxed in the Great Purges as the NKVD found a chief- Yezhov- who was adept at "finding" the evidence that confirmed Stalin's suspicions.
Finally, it is important to realize that Trotsky's fall from grace and eventual exile was a protracted process. He naturally expected himself to be the natural successor to Lenin, so he never really cultivated a following in either the Red Army or the larger state apparatus. Stalin was much more proactive in comparison, building what historians like Sheila Fitzpatrick and Stephen Wheatcraft have called "Team Stalin" of like-minded young Bolshevik professionals. Stalin was much more personally amenable and also competent in his duties. Trotsky had something of a preening intellectualism about him that grated a number of others and won him few partisans. In the case of the army, his acidic commentaries on proposed doctrines cost him the support of prominent military officials like Frunze. Trotsky's demotion in 1924/25 did not lead to his immediate purging and exile, but sent a clear signal to all his star was on the wane. But it was only in 1927 that he was kicked off the Central Committee and even then, it took one and a half years to lead to his final exile. Trotsky had frittered away or lost much of his political capital in this period.
Ultimately, Trotsky's connections with the Red Army was more of a handicap to his political fortunes than an asset. Being involved in military affairs as Commissar meant that he had to wade into postwar military debates. Trotsky's acerbic personality, coupled with his realism about military affairs, meant he had a strained relationship with his subordinates. The spectre of a Bolshevik Bonaparte was one of the several barbs Stalin could use against his rival. The Bolsheviks as a whole were skeptical over the larger loyalties of the military even as the nascent USSR valorized the Red Army and its role in the Soviet state. This meant the Red Army's leaders tended to be locked out of important political discussions and its generals were much more attuned to how vulnerable they were under the new regime. Sticking their heads out for a civilian military chief a number of them did not particularly like would have been a step too far for them, especially given that Trotsky's prolonged fall from power made a military intervention much more risky.
Sources
Erickson, John. The Soviet High Command: A Military-Political History, 1918-1941. London: Frank Cass, 2001.
Fitzpatrick, Sheila. On Stalin's Team: The Years of Living Dangerously in Soviet Politics. Princeton: Princeton University Press, 2017.
Kotkin, Stephen. Stalin. New York: Penguin Press, 2015.
Whitewood, Peter. The Red Army and the Great Terror: Stalin's Purge of the Soviet Military. Lawrence: University of Kansas Press, 2015.