An Absolute Monarchy surviving to this day with a Pod post 1900 is probably ASB, though I have seen it done in one TL. For the Monarchy to survive in any form with no pods before 1900, you'd probably need Nicky and Alex out of the way for whatever reason, as soon as possible. Another option might be to have Stolypin survive-he might be able to reform just enough to keep support until Nicky dies of natural causes, if World War I is butterflied away somehow.
Having the monarchy restored after the cold war is a remote possibility I suppose, though it'd require things to be in more of a mess than OTL I think.