In Augustine’s mind, when did he ever stop being a Christian for there to be a need for him to convert back to Christianity?
No one can read Augustine's mind - don't believe anyone who says they can. But I would surmise that he never stopped being a Christian because he was not a Christian i.e. was not baptized, a requirement for being Christian, until April 24, 387 AD. Note that by my statement that baptism is a requirement for being Christian, I am making a historical, contextual theological statement of what he and Christians around him would have believed. So, unless you have evidence of a licit baptism before April 24, 387 AD, your question is ill-formed.
Surely the source of that would provide an answer, or his own writings?