Real life socks hold by virtue of friction between fabric and skin. This means the sock fabric needs to be pressed to the skin and the coefficient of friction must be large enough. In the cloth room it is possible to set the coefficient of friction per dynamic group but you cannot set a pre-tension. At the start of the simulation the stress in the fabric is zero, so the pressure is zero and hence the friction is zero. Legs are tapering to smaller girth in the direction where gravity goes, so when the fabric 'sags' the chances of building up pressure becomes even less.

A typical workaround is to model the socks around a thinner leg and in the sim first grow the leg to full thickness while gravity is zero. This would generate pressure and hence friction to hold the socks in place during the rest of the sim.