You have opened the drapes to let the light in but the center edge is creeping toward the middle of the rod. It seems as though the drapes are trying to close. This happens because the drapes are gathered into a smaller space than is actually required. Some observation and a few drapery-makers tricks will give you the tools to stop the sliding.
Draw the drapes open as much as possible. The drapes will be tightly gathered or pleated along the rod. When the drapes have stopped sliding closed toward the center, they have reached the point where the tension created by all the gathering has eased enough to allow the drapes to rest. This is their natural resting position. The simplest way to prevent them from sliding is to not draw them past this point.
Extend the curtain rod for drapes that must be opened and closed. Draw the curtains back to the desired open position and measure the amount of space they use on the curtain rod at each end. Measure the width of each side of the curtains after they have slid to their resting place. The difference between the two measurements is the amount to extend the curtain rod at each side.
Install tie-back holders on the wall and use tie-backs to hold the drapes in the open position on drapes that must be operable. Position the tie-backs high on the drape to prevent sliding. The lower the tie-backs are positioned, the more the top edge will slide.
Insert a wood screw into the back of a wooden rod to prevent gathered stationary panels from sliding. Install it toward the center of the rod, at the inside edge of the drapes when they are in the desired open position. Use a 1 1/2-inch screw and leave it extended out from the rod at least 1 inch.
Stick one side of a self-adhesive hook and loop tape dot on the back of a metal rod at the position of each inside edge when in the desired gathered position on stationary panels. Stick the other side of the dot to the inside of the rod pocket of the back side of the drape or the inside of the curtain ring. Put the dots together to prevent the drape from moving.