The battery was draining very quickly, regardless what I did to conserve power. After reading about the expected life of Lithium Ion batteries, I realized what I needed to do. After reading an article in the Wall Street Journal about iFixit and how to replace the battery, I decided to do it myself.
I was able to replace the battery and it is working fine. I had the repair guide up on my computer while I did the work, and I just followed the instructions, step by step, until it was finished.
I had three hiccups. First, I had trouble removing the adhesive strips behind the old battery. Once I figured that out, removing the battery was simple. The second problem came to light after I re-assembled the phone and attempted to turn it on. Apparently, I did not connect the battery plug correctly. I was able to quickly re-open the phone, re-connect the battery cable, re-assemble and start the phone. The phone worked fine after that.
The final issue involved re-charging the battery after letting it discharge below 10%. I plugged it into my regular charger when I went to bed. When I woke up, the battery was still at 8%. Even though the phone indicated it was charging, it would not increase the charge. So, I did another hard reset and this fixed the problem. I was able to charge it all the way to 100%. Since this is the first full charge, I do not know if the new battery will improve my usage time. I will add to my post after using it for a while.
The repair guide was very helpful and easy to follow - with one exception. When removing the adhesive strips from the back of the old battery, the instructions were a little confusing. I think that it would be helpful to explain that stretching the strips actually releases the adhesive. I stopped pulling too soon, and when I started pulling from the side, the strip broke under the battery. I was able to reach it with tweezers and then pull it until it released. I figured all this out after breaking the two outside strips, but successfully removing the middle one. All in all, it was more simple than the instructions made it sound, hence the confusion.