Cobblestone stairs seem to disappear after reloading the game in both single and multiplayer.
I've sent two attachments of the issue, one of the pictures was taken just after placing the stairs down, the other was after reloading the game.
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duplicates 1
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Dupe of MC-87194
It seems unloading the chunk is enough, plus it only affects newly placed stairs. I was working on extending a staircase I had built previously and then went away for a bit. When I came back all the new steps had disappeared but the old ones were still there. Lighting isn't updated so one can still tell where the stairs were placed.