一再 / 再三: repeatedly, over and over
【四08】副词 / adverbs (频率)
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
一再 and 再三 put the verb under the sign of insistent repetition: you remind, explain, promise or postpone again and again. 我一再提醒你不要迟到, 我再三解释，他还是不相信. They go after the subject, before the verb.
一再 often describes a repeated fact that you suffer or complain about: 一再推迟 (put off time after time), 一再保证 (promised over and over). 再三 goes naturally with careful, considered acts: 再三考虑, 再三解释, 再三提醒.
In both, the idea is insistence, not habit. For a habit, say 常常 or 经常; for a plain repetition, 再 or 又; an ordinary trip is counted: 去过好几次.
Examples
我再三解释，他还是不相信。
Wǒ zàisān jiěshì, tā háishi bù xiāngxìn.I explained over and over, but he still doesn't believe me.
他一再说对不起，我也不好意思再生气了。
Tā yízài shuō duìbuqǐ, wǒ yě bù hǎoyìsi zài shēngqì le.He kept saying sorry, so I feel too awkward to stay angry.
我一再提醒你不要迟到，你怎么还是来晚了？
Wǒ yízài tíxǐng nǐ bú yào chídào, nǐ zěnme háishi lái wǎn le?I kept reminding you not to be late. How come you still arrived late?
会议一再推迟，大家都有点不高兴。
Huìyì yízài tuīchí, dàjiā dōu yǒudiǎn bù gāoxìng.The meeting was put off again and again, and everyone is a bit annoyed.
医生再三告诉他不能喝酒，可是他不听。
Yīshēng zàisān gàosu tā bù néng hē jiǔ, kěshì tā bù tīng.The doctor told him over and over not to drink, but he won't listen.
经理再三考虑以后，才同意了这个计划。
Jīnglǐ zàisān kǎolǜ yǐhòu, cái tóngyì le zhège jìhuà.Only after thinking it over again and again did the manager approve the plan.
Common mistakes
✗ 我一再吃早饭 → ✓ 我常常吃早饭 (一再 marks insistence, not habit).
✗ 我一再去北京 → ✓ 我去过北京好几次 (ordinary trips are counted, not described with 一再).
✗ 一再他提醒我 → ✓ 他一再提醒我 (一再 is an adverb: after the subject, before the verb).