I've been able to login fine and trade with Yahoo Open ID with no issue for the past several months (or well, years).
This issue appears to only be restricted to Google-connected accounts. If I recall correctly, Google integration was introduced very late so I assume there are considerably fewer users using Google authentication, but I guess I could be wrong (I'd be using it instead of Yahoo authentication if it had existed when I signed up). Hyuga (I think) has posted to the Monatr Twitter acknowledging the situation - noting that with the sudden influx of activity and lack of manpower (if I recall correctly he only has one other person working with him?) to support Monatr and other projects they haven't been able to resolve the issue yet. There has been no report of mishandling or loss of user funds at this point in time (in his most recent tweet on Monatr, he states that they are intact).
FYI most trading is being done at Zaif.
@Metros This is not the Monaco thread.
@Ukuhudu It was pretty popular, suffered a period of stagnation for a bit, and now is getting a lot of renewed interest as of late.