My experience with the lithium battery in the One-Touch Ping has been pretty good. I suspect that your battery may have been hot or have been part of a very old stock. It isn't normal for them to fail in 2 1/2 weeks.
Be sure you are using the Energizer Ultimate Lithium battery. It is a blue and black pack with a 9x on the front in hot pink lettering. The lithium battery itself will be silver with blue and black lettering and markings. There is a more inexpensive battery available from Energizer, but I haven't used it.
What I do is look at the battery indicator icon on the main menu, just below the time. Fully charged is three squares. When the battery indicator goes to two squares, I replace the battery at the next reservoir change/fill. With the Ping, a complete rewind must be done when replacing the battery.
Batteries aren't worth messing with. Changing the battery when it is necessary will keep your pump running efficiently. You won't loose your pump settings during a battery change. Always carry a spare battery with you.
My batteries usually last four to five weeks.
Welcome to the Ping. I hope you like yours as well as I like mine. Let us know how it turns out. Be well.