Backup LiPo Battery charging circuit
I see a spec of 50mA not 100mA

You may consider an adjustable regulator suitable @2A for around same price. ($0.25/1k) and limit current with a 150mA PTC.

http://www.digikey.com/product-detail/en/richtek-usa-inc/RT9025-18GSP/1028-1008-2-ND/2470042

Then design for 3.7 to Vbat and use a 0.2V Schottky diode@100mA for 3.5 Vout to give more headroom for LiPo drop to 3.2V and 3.0 V min standby

When searching for a better diode, you may have to increase Vf a bit and If x10 then come up with a solution like BAT60A 0.2V@120mA@25'C rated for 3A max ($0.10/1k)

High current rectifier Schottky diode with extreme low VF drop (typ. 0.12V at IF = 10mA. http://www.digikey.com/product-detail/en/infineon-technologies/BAT60AE6327HTSA1/BAT60AE6327HTSA1CT-ND/1557845