Finally, a puzzle that doesn't involve a bunch of counting! Hopefully it hasn't come up before.
What kinds of situations can you think of that involve both players endlessly playing the same moves over and over again?
Don't worry about the likelihood of them actually getting there.
For example: KCx2, Monumentx3: Both players are getting 9 VP a turn. Unless some other power cards are around, nobody wants to break it.
Or, all the coppers are trashed, and nobody has treasure or gainers.
Or, Highway, KC,Smugglers, and Colonies, plenty of draw, and no + buy.
There are surely many more subtle ones.