The fact that I know in advance that this is meant to apply only to Rome and those in communion with Rome really sours me on the idea that 'infallibility' as understood by Rome is something given by God, rather than invented by man in an attempt to substantiate the supposed divine command enjoyed by Rome according to its defective and heterodox ecclesiology.
'Speaking' as a member of the first Papal Church in the world (which is Alexandria, not Rome; look up the history, particularly as concerns the thirteen bishop of Alexandria, HH St. Heraclas), it is notable to me that we have never, ever declared any such thing or received any such thing from our fathers. It is an utterly foreign idea, and no one in our Church would stand for it, if it were proposed. The truth is (and I know RCs will disagree with this in advance; that's fine) that keeping everything so that no bishop is infallible in any circumstance is something that actually protects the Church, while Papal infallibility as the RCC teaches it actually harms the Church. It is not the divine protection that they think it is. Why? Because sometimes Popes 'go bad', obviously. I'm not going to name the obvious ones that you'd think, given my ecclesiastical allegiances, but I can name some of 'ours' (that is to say, Coptic Popes), such as Pope Yusab II, who was a shockingly recent example (r. 1948-1956) of a Pope who needed to be removed from office for the good of the Church and the protection of the faithful, as he had proven to be a dangerously ineffectual leader, and was in practice being led by a cadre of intermediaries that surrounded him, controlling access to him, engaging in simony, and doing all kinds of other things to further weaken him, and ultimately doing great damage to the Church in Egypt at the time. I could make similar, even more recent examples of people in other communions like the former Patriarch of Jerusalem Irenaios (for an Eastern Orthodox/Chalcedonian example), who was deposed in 2005 following some shady property deals with Israeli developers. Truly Rome is alone among the ancient churches in believing this fiction of infallible leadership; and that is what it is -- a fiction.