Weed that won’t die
This weed is common purslane. It is an annual plant, which means it sprouts from seeds in the soil each year. It is important to remove it before it flowers and sets seed, so as to reduce the problem. Your soil is probably holding many years worth of seed, so a pre-emergent herbicide can help control it. If you put down crabgrass pre-emergent control that helps.
There are a number of herbicides labeled for controlling purslane. There are post-emergent herbicides available, as well. Always follow the label directions and precautions carefully.
Here is an article that describe s control options. Here in Michigan we have cool-season turf such as Kentucky blue grass, fine fescue and perennial rye. If you treat purslane in your cool season turf, be sure to use the chemicals safe for those grasses( i.e. do not use chemicals listed for warm season grass turf).