Even if there isn't any obvious cable damage or bulging, the adapter could be failing. If the adapter is not one of the newer L-Shape Magsafe plugs, the need for a SMC firmware update is moot, but it's helpful to have the system up to date regardless.

Have you confirmed if a second, known-good adapter works on your Mac?

Updated: An SMC reset can also correct magsafe LED issues. http://support.apple.com/kb/HT3964

Since Apple doesn't publicly commit to power levels or even pin compatibility on the lightning connector, anyone interested in learning how hardware should be designed to work with Apple's dock connectors could choose to join the MFI program:

• https://developer.apple.com/programs/mfi/

As a developer, Apple will provide you with detailed hardware requirements, schematics and even technical support. I haven't seen anyone take a current meter and volt meter to the devices and post publicly, but wanted to make you aware of one official avenue to get this sort of information across all of Apple's iOS product line wether they use the 30 pin dock connector, the lightning dock connector or some of the other specific iPod connectors.

Additionally, the pin out for lightning connectors requires an authentication chip according to wikipedia, so getting power out of a lightning device involves software authentication before power will flow.

The article describing 8 pins that are active (both above images are from wikipedia) indicates that when power flows into the phone (the opposite of your use), pins 1 and 5 are ground and power respectively. However, until your cable identifies itself to iOS, no power will be provided.