Generally it's been a phased out position all over the NFL.
The QB driven, dink and dunk, spread offense type shift is partly because of the rules that favor offenses now. Part of it is because there are more talented and efficient QBs than in eras past. People forget but there was a good 15 year QB drought in the NFL where maybe 6-7 teams had good QBs and everyone else had scraps. I mean there was a time when the 49ers had Montana, Young and Bono and all ended up starters in the league. When your third stringer can start on a playoff team in the NFL for several season, that should show had bad QBing was in the day. If you don't have a good QB, you have to try to win on the ground and for that you need more snaps for a fullback when your focus is ground and pound.
The continued loss of the traditional West Coast Offense, where the fullback is a versatile and important offensive position, ( Shanahan is back, Holmgren is, to some degree, back in principle, but before that, a lot of WCO guys were gone, Mooch, Gruden, Rat Face, Holmgren, Seifert, etc) helped to phase out the fullback. A lot of coaches have come out of Andy Reid, one of the last surviving WCO coaches, and he has no commitment to any fullback, so why should his prodigies?
It's not just about talent shifts, it's also about coaching trees. If you're an assistant under a head coach who does things one way, it's how you learn, its what you will probably implement.
I also think the limited roster spots combined with the growing importance of certain positions created a roster numbers crunch ( Nickel backs are essentially starters in todays pass heavy NFL. 3rd down/COP backs also play much more than they ever used to do. Long snapper is a legitimate specialist position now. Also cap issues force more younger and cheaper players to fill the ranks of rosters where versatility is very key. Part of the reason Woodhead got cut by the Jets is the team felt other players might be more versatile and help at several different functions in comparison.) And fullbacks got hit in that crunch.