I am posting this to the web in case it helps anyone else trying to troubleshoot a similar problem.
Recently I noticed my iPhone’s battery was ending each day significantly lower than usual, causing me to have to charge it every night instead of every couple of days. At first I suspected the extra consumption was caused by communicating to my Pebble smart watch but quickly eliminated that possibility when turning the Pebble off for a day had no effect.
After some experimentation, the change that restored my battery usage to its previous norm was disabling background apps refresh for Google Maps. This was an application I had recently installed because it works very, very, nicely with the Pebble, sending turn-by-turn navigation directions to your wrist as you walk. This completely removes the need to take the phone out of its pocket every few minutes to double check that the road you just passed was not the one you were supposed to turn down! However I do not use it frequently enough to justify doubling my daily power consumption…