A JKR Pottermore writing says yes, it can.
In a writing on Pottermore, JKR says that someone’s Patronus can change form due to at least three different reasons: if they suffer a loss, fall in love, or their personality changes a lot.
The form of a Patronus may change during the course of a witch or wizard’s life. Instances have been known of the form of the Patronus transforming due to bereavement, falling in love or profound shifts in a person’s character. Thus Nymphadora Tonks’s Patronus changes from a jack rabbit to a wolf (not a werewolf) when she falls in love with Remus Lupin. Some witches and wizards may be unable to produce a Patronus at all until they have undergone some kind of psychic shock.
Patronus Charm (Pottermore)
According to this, then, it wouldn’t necessarily require external circumstances for someone’s Patronus to change - a significant change in personality can be enough. So yes - a Patronus can change over time.
Valorum’s answer already covers whether Snape’s Patronus would change, specifically.