What are these weeds? I've been hitting them with 3 way (2,4-D, Quinclorac, and Dicambia by Bayer) a few times now but they seem to persist. I'm using the "home owner strength" of the 3-way so the %'s are lower than the professional kinds.
Looks like common chickweed (Stellaria media). This is a winter annual, with seeds germinating in late fall (maybe very early spring in the northern US). Spraying it with a weed killer now will be totally ineffective, as it appears you've already found out. The best way to control it is by having a thick, healthy lawn, mowed high (around 3" is now the recommended height for residential lawns). The seeds need sunlight to germinate, so if you have a thick, tall lawn it's unlikely that enough sunlight will hit the ground to germinate the seeds.
You could try a pre-emergent in late summer to prevent the seeds from sprouting, or spot-spray with your herbicide in spring, as soon as you see the new plants in the grass.
As weird as this sounds, you could also try deadheading it when the seeds have formed and before they drop, but this may be too late in your area.