How long does it take for the "Give Valentine" to reset on your neighbor's character?
Generally they clear when they get collected.
An active player will get the hearts more quickly, thereby clearing any characters with Valentines right after they have been received.
If someone is less active, you may not be able to give them Valentines because their other friends have already filled up all of their characters.
Since the update is relatively recent, it's possible you can't give Valentines to some players because they may not have updated their game to the newer version yet.