i have a standard jazz bass, very nice. i recently put a new set of strings on it. same gague E string i always use (1.05), and for some reason, it refuses to stay in the slot at the nut

. i'll hit an open string and it will pop out. i put a flatwound .95 gauge e string in temporarily, its staying in better, but still goes out, and pops right out as soon as i put in in drop D. is there any way i can file away parts of the nut or something to fix it, or do i just need a new nut...new neck? (please no, i have no cash)
HELP HELP!!!
-punkbass479