You should never allow the battery to drop below 40%. If you've been dropping it below 15% for a long time (the phone came out over 2 years ago), it's surprising that it lasted this long. (You also shouldn't charge it to more than 80% if you want it to last a long time.) It's probably time to replace the battery - and start treating it properly. (Lithium batteries were chosen for cellphones because lithium is the lightest metal [except for hydrogen around absolute zero], not for their ability to be deeply discharged. For that you'd need a gel cell, and that would weigh more than the phone - and be as large.)