Is it outdoors or in a window or greenhouse where it might have been exposed to unusually cold temperatures? That would add another possible cause. (Comes to my mind as a possibility because large part of the eastern and central US has suffered unseasonably cold weather recently.)
Dig a finger down into the soil in the pot.
Is the soil in the pot wet (and maybe has 'off' odor)? This is bad. If some sort of fungal root-rot has set in, the basil may be doomed.
Or is the soil dry? When potting soil gets too dry it can be hard to re-wet. Water tends to run right through the pot rather than be absorbed. In which case, you need to set the pot in a bucket of water until it fully moistens.
The too small pot issue makes the probability of being too dry too often a likely thing.
If the basil does recover, it would be best to re-pot it in a more appropriately sized container.
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