This does not clarify if or why this sense of identity is again formulated or again appears after it is eroded. Why, if it is washed away over time, does it reformulate?

The sense of identity keeps reformulating until one becomes an arahant and attains nibanna. There is another analogy in Buddhist suttas that describes the sense of identity like the skin of a pig. Through the practice, the sense of identity is "skinned" off and it can never attach or stick back. I am not qualified to elaborate on this.

Even the sense of identity which we currently  use and identify with is constantly arising and disbanding.  To believe this, you have to experience it with keen mindfulness.

Seen by whom?  The cognizing feature of mind essence, sees. 

If the seer is merely a passing phase of whatever, then how is it that this passing ephemeral whatever makes declarations about consciousness over a certain time, as for example Buddha’s life of declarations about his Way, or some other Buddhists teacher who is declared to be enlightened?

Even a yogi who attained nibanna is required to live out the rest of the current birth, reaping good and bad consequences based on  his/her prior actions in samsara. This is called nibanna with residue.

To put it bluntly, does the sense of identity erode once and for all or not?

I guess it is more accurate to use the skinning of the pig analogy.  In this case, the stickiness, the binding of the pigskin to the pig body is totally loosened and it stays on the pig body until the death of the creature form. I'm sorry to use such a crude example.  

What was once regarded to be a solid identity, a ME,  is now seen as a constantly changing, coming and going of mental factors.

Seen by whom?

Seen by the innate congnizing nature of mind essence.

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  I've answered the best I know how and I'm sure there are some inconsistencies with actual Buddhist doctrine.  I shared the experience for the sake of sharing what actually happened.  I try not to overthink stuff that happens in meditation. Talking about it and trying to make sense of it eventually causes me to lose touch with the actual experience and the guidance it was meant to yield.

Discussions about the permanence of the sense of identity usually become combative on this forum.  There is no need for that.  We need to get direct experience and follow where it leads. Disputing with words  fuels speculation which circles round and round.