Wilting is of course a sign of water stress, but the question is what is causing this. It could be dry soil or soggy wet (poorly drained) soil in that pot. If the plant is in more sun that could be the reason it is wilting faster. Then there are root diseases and nematodes (cause swollen knots on the roots) which can't be controlled practically. If they are in a container you just toss the plant and soil out in the trash and start over for these last two. If they are in the soil then don't plant tomatoes in that spot in the future.
The white eggs could be many different insects so I don't know what you were seeing there. If you see insects on the plant take a photo or some insects to your County Extension Office for identification and control recommendations, if needed. If your tomato looks like it won't recover I'd take the plant with its roots attached to the Extension Office for diagnosis. Do this before it is totally dead so they can effectively diagnose it.
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