If you are referring to the battery life between charge cycles then it depends on use but you should be able to use it 2–3 months between charge cycles.
If you are referring to the battery lifetime then it depends on how many charge cycles* the battery is rated at. Apple does not state how many charge cycles the Siri remote is rated at but to give you some context. Apple states that the iPhone battery is designed to retain up to 80 percent of its original capacity at 500 full charge and discharge cycles and the MacBook Pros and Airs should retain the same 80% after 1000 full charge and discharge cycles.
Based on that, even if the Siri remote was only rated at 250 full charge and discharge cycles before it got down to 80% capacity and you charged it 12 times a year due to heavy usage the battery should retain 80% of its charge after 20 years. In other words the battery should last longer than the useful life of the Apple TV. But then again YMMV!
*Apple states that a charge cycle means using all the battery's capacity, but not necessarily by full charge and discharge; e.g., using half the charge of a fully charged battery, charging it, and then using the same amount of charge again count as a single charge cycle.
