The general answer is yes, they do stick around.
Now when enormous monocultures are planted in legumes, there couldn't possibly be enough carry-over so that each plant will get a good dose, so that is why you see pre-inoculated soybeans. Also, it may be possible that all that herbicide/pesticide/fungicide that the farmer sprayed last season made it hard for any beneficial commensal bacteria to stick around. So they inoculate.
But enough about those people in industrial agriculture. In the Permie world, we are constantly inoculating our plants, our soils, our waters. We want the diversity that is the diametric opposite of monoculture. You can inoculate by having a bird feeder and encouraging wild birds to drop their little packets of inoculate on your garden. You can inoculate by hauling in swamp water and watering with that instead of city treated water. You can inoculate by taking a walk in the woods and collecting mushrooms and blending them up into your
compost tea. But whatever you do, don't wait until next year to inoculate.
