There's two sides to the battery story. You can never let it die AND still put it through its paces with prolonged charging cycles, higher wattage charging, hot environments, phone usage during charges..
Many factors come into play when battery health is on the table. The reality is, your phone is old. Well, your battery. Even with perfect use, you'd be discovering weak spots or inconsistencies.
Your solution is to buy a battery replacement. Get a nice one, preferably with a bigger capacity than your stock (if offered).
Edit: To answer your question, failing batteries have big trouble handling voltage spikes if the reading isn't correct (ie, going from idle to say, watching a video). The response is to shut down. Its a safety mechanism.