。
She was so overcome with emotion that her voice trailed off into a whisper.
Literal
She [topic-は] emotion-overwhelmed [so-て] voice [too-も] faltering became.
感極まる ('to be overcome with emotion') uses the verb 極まる ('reach the extreme'), which attaches to nouns of feeling or condition to express their utmost intensity (感激極まる, 苦極まる). The te-form connects cause and result with characteristic Japanese tightness. たえだえ (途絶え途絶え, often written kana-only) is a reduplicated state-mimetic for something faltering, fading, or breaking up — a voice 'on the verge of being cut off.' ~になる pivots the description to a change of state: her voice *became* faltering. The も in 声も signals 'even' / 'as well' — implying that other faculties (poise, composure) had already gone, and now even her voice was failing.