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Every time I replay it, I can't help finding her reactions totally adorable.
Literal
Replay do [each-time-度に], her [genitive-の] reactions [to-に] one-by-one moe [end-up-てしまいます].
Otaku/fan vocabulary in full effect. 萌える (moeru) is the set verb behind the otaku term moe — literally 'to sprout/bud' (like plant growth), but in fandom slang it means 'to find [something] irresistibly adorable, to be fondly infatuated with a character trait.' 萌えてしまう uses ~てしまう ('end up doing,' often with a note of 'can't help it') to frame the emotional reaction as involuntary — 'I just can't help it.' いちいち ('each and every one,' 'one by one') is an adverb that here functions emphatically: 'every single reaction sets me off.' The 度に (たびに) pattern ('each time X') marks the recurring trigger.