First determine the length of the Chase:

• Standard: Five rounds, used for most chases and usually simulates less than a minute of action per turn.
• Extended: 10 rounds, used for long pursuits such as those that take place between ships, and may be measured in minutes, hours, or even days.
• Dogfight: The “chase” is actually a battle with highly mobile participants. It ends only when one side or the other withdraws or accomplishes its objectives.

At the end of the last round, any prey who haven't been otherwise stopped or captured escape and the pursuit ends.

Savage Worlds Deluxe Edition p. 94