There are several things that could be going on. If your beets or turnips were planted too early in the spring they may have had enough exposure to cold weather to begin bolting (fcapsullowering). You will be able to tell if this is the problem because the plants will begin growing a tall flower stalk. If they do this they will never make a storage root.
Another possible problem is that the plants are too close together. For beets each "seed" is actually a capsule that contains several seeds. Beets therefore need to be thinned to one plant every 4 inches after the plants are about three inches tall. Turnips should be thinned to 4 to 6 inches apart after emergence. If plants are too close together they will be to stressed to produce large storage roots.
Finally, some turnip varieties were bred for greens production and do not form large storage roots. If you happen to be growing one of these varieties it will not produce a storage root.
If you want to grow turnips and beets for a fall garden this year try planting beets in early August and turnips in late August or early September.