Well, as the question says, and with no specific POD, can we have Novgorod survive intact at least for some more 200 or so years after its historical annexation by Muscovy? We can work with High Medieval PODs here, I just want to discuss the circumstances that led to its apogee and later demise.
Considering that it survived the Mongol invasions, and the expansion of the Teutonic Knights, I see that the causes of its downfall occurred much later, by the late 14th Century. But then what, would butterflying away Muscovy's ascension be enough to preserve it, or was it bound to be incorporated to other monarchical Russian principalities?
To start with, it did not “survive” the Mongolian invasions as an independent state: it was not taken and looted because it, as some other entities, voluntarily accepted Mongolian rule and paid tribute. Then, there was no real “expansion” of the Teutonic Order in this direction because Teutonic Order was on the wrong side of Lithuania and Novgorod had to deal with its weak branch, the former Livonian Order, which simply did not have numbers needed for any serious expansionism even if it was not in a state of the never-ending quarrel with the archbishops of Riga and other local entities (in the over-advertised battle on Lake Peipus novgorodian opponents had been led by the Bishop of Dorpat and while the Teutonic/Livonian knights numbered approximately 100, there were at least 1,000 Estonians: Novgorodians had been looting their land). Then, of course, there was a buffer, Pskov, which had to be taken before getting to the Novgorodian territory. And, if push was really coming to shove, there could be an appeal to the Khan: at least on one occasion the threat of the Mongolian involvement put the planned “crusade” to an abrupt end.
Would he be able to survive? Your framework is not quite clear: are you completely eliminating raise of Moscow and if yes, then what is the alternative? Some other Russian principality? Greater Lithuania?
Anyway, most probably Novgorod was going to lose to any alternative candidate. First, it’s military power was quite limited and its quality low: in OTL main Novgorodian army was defeated by a small detachment of the Tatars on Moscow service. Second, it’s economic strength was linked to Hansa but Hansa was going down due to the Danish and Swedish activities on the Baltic and in the changed situation Novgorod was not even conveniently located: in the later years Narva became the main outlet for the Russian imports/exports and Narva is much easier to reach from Pskov. It should be telling that during few centuries of controlling a piece of the Baltic coast Novgorod did not establish a port there and did not even try to build its own modern ships: all goods had been carried by the Hanseatic merchants.
