Worms and snails come to mind as culprits. You could mix some Bt (Bacillus thuringiensis) into your foliar feed mix to spray on, or a watering can and pour it over your plants, and if snails are a problem a sprinkle of Sluggo will get them. If pill bugs are there, Sluggo plus has spinosad and will solve that problem. And the spinosad will work on several other pests as well.
You'll see snails if you put a shallow bowl in the garden and put in some fresh beer. Overnight they will find the beer and die happy in it. I've done that over the years, but once I discovered how well Sluggo works, I keep the beer for the gardener and not the garden.
Here is the
Basil entry from the Natural Organic Library.
I have an area where basil comes back every year, from the seeds of last year. I've had to pull grass from around the seedlings and sometimes they need transplanting to spread them out - do that when they're tiny (an inch or two) and they won't even slow down in their growth. Once the plants get bigger and more fragrant they seem to be left alone - probably the strong scent is enough to repel pests.