Is there a trick to recharging the battery. I have purchased two batteries and can't get either one to recharge.

There definitely shouldn't be a trick. When one of our lithium batteries is plugged into a processor board and USB shield, and a USB cable is plugged in, it should charge- unless it's already charged. The amber 'CHRG' LED should turn on while charging, and off when it's done or not charging. What are you seeing with yours?

It turns amber then goes off but it is not charged. Both batteries lasted about a day but afterward they will not recharge.

It only stays amber for a few seconds.

I don't remember hearing about a case like this- You've tried it from multiple USB power sources? Might be time to send an email to info@tiny-circuits.com with your address, and reference this thread.