Quoting from the HP Wiki article on Tobias Snape:
Tobias had a very poor relationship with both his wife and his son; when Severus was younger, Tobias frequently shouted at and hit Eileen whilst Severus crouched in a corner, crying. The memory of watching his parents fighting would haunt Severus even into adulthood, as witnessed during an Occlumency lesson given by him to Harry Potter.
It is likely that Tobias was equally abusive or at the very least neglectful of Severus, given how much Severus despised all Muggles. Even at a very young age, Severus noticed with pain how his parents fought; it caused him a great deal of distress, and he was quite happy to be able to leave the house to visit his friend Lily Evans.
The fact that Tobias lived near a textile mill may have given some indication of his occupation or socioeconomic status. Tobias's eventual fate is unknown, although it is likely that he had died by 1996. Tobias may have been an alcoholic or drug addict, or might have been unemployed, given how he frequently abused his wife and son, lived in a slum neighbourhood and his son wore ill-fitting, dirty clothes.
That all being the case, what prevented Severus Snape from becoming an Obscurus?