Now this one is a really tricky one. To be completely honest with you I think that Muscovy can fail to take Kazan in 1552 but overall Muscovite conquest of Kazan is pretty much inevitable.
The reason is pretty simple – even by XV century Muscovy has several times larger population and much more developed economy. While tactical successes can buy Kazan some time strategically their situation is desperate.
Moreover even peaceful coexistence is more or less unfeasible. While most Kazani population is settled the ruling class consists of Tartars whose primary (or at the very least major) occupation for several generation was pillaging and extorting payments from Russian lands. Unless they suffer major defeats they are very unlikely to stop (in OTL even regular loosing wars and submission to Muscovite terms every 20 or so years didn’t stop Tartars from raiding). Even if by some miracle local elites decide to discontinue raids it would only demonstrate Muscovy Kazan’s weakness and increase the desire to annex/put under tight vassalization.
The only deal that can both satisfy Muscovy and let Kazan remain intact for the time being is something akin to OTL Muscovite-Qasim Khanate relationship. But a) it was exactly what Muscovy repeatedly tried to enact and that for some reason was completely unacceptable to local elites b) it is probably not what OP wants since Kazan by such settlement would definitely have no foreign policy of its own, would probably lose a substantial portion of its territory to Muscovy proper and would eventually be annexed by Russia like Qasim Khanate was IOTL.
One could argue that Crimean Khanate was in similar circumstances and yet managed to hold on until second half of XVIII century. However Crimean Khanate had two invaluable advantages that Kazan Khanate didn’t have.
1. Logistical inaccessibility. Crimean Khanate was separated from settled areas of Muscovy and Grand Duchy of Lithuania by 1000 km strip of unsettled steppes without any good communications that could support a large European army ( Don doesn’t really get you to Crimea while Dniepr had portages that allowed Crimean army to effectively block water transport movement). Moreover Crimea is virtually an island in a sea that is completely dominated by Ottoman fleet (thus allowing Crimean and Ottoman forces to use sea transport and preventing enemy to do this) and has basically two points of access both of which were fortified and well-garrisoned.
So you see that Crimea is a really, really hard nut to crack. The only reasonable strategy against it that Russia was able to implement IOTL is to slowly, generation by generation, reduce this steppes gap by settling a northern fringes of it and erecting a continuous fortified line (abatis line, Zasechnaya Cherta in Russian) that defends it and is able to reduce the effect of raids. Only when settled and fortified area reached Dniepr portages Crimea become reachable by Russian armies.
BTW this is the reason why I personally am really, really skeptical to any PODs or butterflies allowing Russia to crush Crimean Khanate before say mid-XVII century (e. g. cliché one where Ivan IV by some reasons decides to crush Crimean Khanate instead of Livonian War and triumphally accomplishes it) - while settlement up to Dniepr portages can be spead up it cannot take much less than 100 years and without such settlement Russia cannot realistically supply an army in Crimea sufficient to crush it.
Having said all this about Crimea let us look at Kazan. It lies on Volga - a major water artery less than 400 km from core Muscovite territory (all of which from Kaluga and Ryazan to Yaroslavl and Kostroma, from Rzhev and Tver to Nizhny Novgorod including Moscow itself is in this artery’s drainage basin). Can supply line to Kazan be even more convenient to use? Well, yes if you build one or two fortresses between Nizhny Novgorod and Kazan. This is exactly what Muscovy did IOTL with building Vasilsursk in 1523 and Sviyazhsk in 1551 and I don’t see any realistic ways Kazan can stop this from happening IOTL.
2. The second major Crimean advantage is that it had a “Big Brother” Ottoman Empire that could always step in if things became fishy. Ottoman Empire also provided Crimean Khanate access to modern weapons and artillery (as well as trained infantry and gunners for Crimean fortresses), fleet to defend its shore, market to sell its goods (mainly slaves) etc. etc. The shear military and political power made conquest of Crimean Khanate an extremely challenging task even when it finally became logistically possible (IOTL after many unsuccessful attempts it took Russia one crushing victory over Ottomans to vasslize Crimean Khanate and another one to finally annex it).
Kazan OTOH lies on the Muscovite side of 1000 km steppes gap. While IOTL they tried to swear allegiance to Ottomans it lead to nothing – even with Crimean support Ottomans couldn’t project force to either threaten Muscovite core territories or reach Kazan (even much closer to Ottomans and much further from Muscovy Astrakhan already was an extreme logistical challenge for the Turks; while with proper Crimean Khan support the 1569 campaign could probably achieve some form of success, Astrakhan would be reconquered by Muscovy shortly after because of logistical reasons).
All other neighbors of Kazan are much less populous and powerful and cannot really shift the balance between Muscovy and Kazan Khanate.
Muscovy of course had other enemies but I find longterm alliance of Kazan with say Lithuania or Sweden extremely implausible. Even if such alliance somehow could have been forged Muscovy lies between Kazan and its potential allies thus any sort of meaningful coordination beween allies is impossible.
IOTL Muscovy had all sorts of disasters when trying to subjugate Kazan – bad luck (in 1478 when bad weather helped Kazan to survive), faulty strategy (in 1487 Muscovy had taken Kazan but instead of annexing the state simply put pro-Muscovite ruler to govern it; of course soon after Russian troops left he quickly became anti-Muscovite), inability to push when necessary (in 1507), tactical mistakes (in 1524 when supply train for besieging Kazan troops was insufficiently guarded and thus destroyed by Kazani) even shear idiocy of high command (in 1530 Muscovite troops waited for whole day at Kazan’s open gates until two supreme commanders of Muscovite argued over who of them should enter Kazan first; after several hours of inaction Kazani finally decided to close the gates)
The fact that after all possible mistakes and mishaps Muscovy was still able to conquer Kazan is in my eyes a testament that such conquest was inevitable.
Having said all that one of course can explore early enough PODs that prevent one principality dominance over the Great Principality of Vladimir lands which would allow Tartar states to play smaller principalities against each other and thus shift balance in the region dramatically possibly allowing the existence of Tartar states for several more centuries.
But since by late XIV century Moscow dominance is pretty much a done deal and Kazan Khanate wasn’t even founded before 1437 I think this disqualifies any such PODs for OP’s intention