If you are going to store a jar of ready-made sauce in the refrigerator, I would recommend using vinegar versus lime juice. Using white vinegar would keep the sauce good in the refrigerator for 3-4 weeks easily.
If you are using lime juice, it would last for about 1 week.
Add garlic and chili peppers right before serving versus adding it to your jar. Any fresh ingredients you add to the sauce will decrease its life shelf.