Short answer - yes, the Frightened condition is still in effect after the death of the caster, and the caster is the source. Like most spells, they end when the duration is up, regardless of the status of the caster. Cause Fear has a duration of 1d4 rounds (or 1 round on a save).
Here is some interesting extra information to consider, though - even though the effect is still in place, the target will actually stop fleeing once they are out of sight of the cause of their fear.
Fear effects are actually defined in a couple of places in the Core Rulebook. The one most people look at is the Condition listing, starting on p565 (Frightened is on p567). This is also the text quoted in the Condition summary on d20pfsrd. However, Fear effects in general are also talked about in the Glossary, on p563 (or online at the Paizo PRD), also found on d20pfsrd on the Special Abillities page. This version of Frightened says, in part -
Other than that stipulation, once they are out of sight (or hearing) of the source of their fear, they can act as they want.
Panicked is slightly different, but says
Once they are out of sight (or hearing) of any source of danger, they can act as they want.
So, depending on HOW the caster died, the target might not have to continue fleeing. For instance, if the caster was disintegrated, or swallowed whole, or in some way moved out of sensory range, the target can stop. Note that they will still be suffering the same effects as Shaken (i.e. -2 to most d20 rolls)
