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Sometimes when she gets going on the issue, she completely loses herself.
Literal
She [topic-は] that issue [object-を] discuss-begin [when-と] self [object-を] forget-ends-up [sometimes-ことがある].
論じる ('to argue, debate, discuss') is a formal, slightly academic verb — more weighty than the everyday 話し合う. Combined with ~始める ('begin to'), it gives a compound verb 論じ始める ('start arguing'). 我を忘れる literally 'forget oneself' is an idiom for being so absorbed in something that you lose track of yourself or your surroundings — the kind of trance a passionate debater can fall into. ~ことがある marks habitual occurrence ('there are times when'), and the conditional ~と signals near-automatic causation: as soon as X happens, Y reliably follows.