The daily attack limit resets 24 hours after the first attack, but the rival record doesn't reset as long as the two players continue to interact with each other. For example, a player could be attacking you a bunch one day, then only Pistol Whipping or Bountying you over a 24 hour period until the timer resets. This would keep the rival record going, and once that 24 hour period elapses, they would be able to keep attacking and each of those would be added to the rival record.

The rivals record also shows "in one day" up to 47.9 hours after the first attack before switching to "two days", so that can also cause confusion.