LM3405 (buck driver) dropout
The dropout voltage is dependent on the converter maximum duty cycle among other things. This is the first thing I check when choosing a buck regulator; some regulators have more complex issues (such as minimum switch on and off times)

This device lists a minimum of 85% and a typical of 94% on page 3 of the datasheet.



The minimum is the value across the full temperature range (-40C to +125C Tj) and is what we would use in a design. 

As the duty cycle in a buck converter is simply Vout / Vin to a very close approximation, then Vin(min) is simply Vout / duty cycle. The datasheet does has guidance for this specific device on page 13 to calculate a more accurate duty cycle for given conditions.

For your 3.2V output (assuming you have measured the output voltage of the converter to ground) that equates to a minimum Vin of ~3.8V (for guaranteed operation) ignoring other parts of the conveter that may need a higher voltage.