Also experiencing this, solo, on Xini (Eris).
I agree that it looks like rounds are being skipped.
1st round played, A reward correctly received.
2nd round, reports 2nd round ineligible but provides a B reward for the 3rd round (that I've not yet played).
3rd round, reports 4th round ineligible but provides a A reward for the 5th round (that I've also not yet played).
I assume the ABAB pattern would continue. For Xini, this is oddly beneficial as when looking for the B/C reward (which are identical on Xini) but is still very much broken.
I have a feeling that the "ineligible" flag on the round is not the real bug.
In any case, I've reported it as an issue to Warframe Support. I suggest you all do the same.