Ja nigdy nie przestałam cię kochać. Nawet przez sekundę.
Both are correct but in this particular sentence most Poles would say "na".
"Przez" is definitely correct and more elegant, whereas "na" tends to be colloqial in this context. IMHO.
Perhaps more Poles would prefer 'na' against 'przez' here, perhaps not. My view is most of them would say 'przez' in this particular couple of sentences translated by Wulkan.
I wish you luck with your relationship but be ready for getting cheated. I know lots of girls are hiding secrets(little or big) Someday(months/years. whatever) you will see Im right(or maybe you will not learn) Mark my words.