A Li-Po cell is 4.2V when fully charged and its voltage slowly drops to 3.2V as it is used. With a 3.2V input then the output of an LDO will be less than 3.2V.
Your circuit must disconnect the load on the Li-Po cell when its voltage drops to 3.2V.
A prefab buck-boost regulator is nice, but they're pricey:
**broken link removed**
I once just used a diode in series with the battery to drop the voltage ~0.6V. The 3.3V parts I was using ran at a slightly lower voltage just fine, so it worked out...in other cases it may not be such a good idea!
MAX6897 is my current option. Its an adjustable supervisory ciruit. So I can set for 3.3v on the lipo and use it to control a hogh side load switch ic.
Basically if power on lipo reaches 3.3v then cut off lipo power tp regulator via high side load ic