Have you fertilized it? It may not be getting the nutrients it needs for growth.

What kind of soil did you use to replant it? You may need to change out the soil. Also, basil likes it dry so not too much water! Give it a couple days of drought then water it. I would not suggest fertilizer at first because an unhealthy plant can became worse with fertilizer. The worst case would be Fusarium Wilt disease. In this case you can kiss your African Blue good bye.

Could it have been potbound (rootbound)? If the roots were matted against the sides of the pot when you repotted it, the matted roots needed to be teased out so that they could resume growing outward.

Sounds like overwatering is the more likely culprit, though. As howlingwolf says, basil doesn't like too much water. Let the top inch of soil dry out between thorough waterings.

Another possibility is that the "soil" it's growing in has too much peat, which tends to repel water when it's allowed to become very dry. If water runs off immediately when you water the plant, immerse the pot (up to a couple inches from the rim) in a clean bowl or saucepan of tepid water and let it stand there for ten minutes to soak up the water. You only need to do this once  then go back to the "top inch" rule.

I add a drop of dishwashing liquid to the water when I soak dry pots. It breaks the surface tension on the potting mix so water will be absorbed. Sometimes the medium will still stay dry if you just soak in water for even an hour.

Basil's are annual's - maybe the place you bought it potted it in a green house to early.

If it flowered and you didn't cut off the bloom's immediately it might just be out of it's lifespan pre-maturely.

Unless you are going for seeds - always cut your annuals flowers immediately - it prolongs the production life of the plant.

Most are, but African Blue Basil is a perennial.