How might you use a LiPo battery as backup for mains power loss?
There are a number of ICs that will do these functions. I would go to the Maxim and 
Linear Technology sites. The downside is that most of these devices is that they 
are only in surface mount packages and a lot of them come in packages without leads (QFN, LGA).

A part like the LTC4088 is nice. It has an input for the battery, an input for the
USB (or wall adapter) and a switching regulator. 

You could also use separate ICs (but you are probably better off with a single).
There is a device that Linear Tech calls a PowerPath controller (LTC4412)
that performs the switchover function. You could add a MAX1555 Li-ion charger
for a low cost charger and add the LTC4412. Also there are devices called "Ideal Diodes"
that will perform switchover. These devices are FETs so you get a much
lower voltage drop than a Schottky. 

The best solution depends on a couple of things you haven't mentioned -- system current,
battery capacity and recharge rates.