Did you change your strings recently? If so, I'll bet you clipped them too short, or the winding of the string is leaving the peg too high up. The strings need to come off the peg closer to the wood of the headstock; otherwise they don't put enough pressure on the nut and can pop out. Check this on your bass before you do anything drastic, permanent, and possibly unnecessary.
As a good rule of thumb, I measure 5" past the peg to clip the strings on basses with bit tuners (Schaller style, like you have), but on the A string I measure 8-9" past the A string peg, just to make sure I have enough winds going around the peg to hold the string down. Give it a whirl.
Oh yeah - if you HAVEN'T changed your strings, it may just be that the strings are sliding up the posts on their own, and a little loosening/readjusting/tightening will fix the problem.
The only other thing that it might be (and I suspect you'd have noticed something was wrong by now) is the neck adjustment. I know it sounds strange, but if your neck is really badly bowed forward, like it's getting harder and harder to push the strings down as time goes on because the neck is bowing (a dry, perfectly air-conditioned environment can do this), it can cause the headstock to come forward enough that the downward string tension on the nut isn't sufficient. This is rare, but I've seen it at least twice.