Overheating Boost Converter
The S1JB-13-F diode has a pretty slow reverse recovery time (trr is 1.8us typ, 3us max).  The boost switcher appears to be variable frequency, but at some loads it's switching frequency may be uncomfortably close (or right on top of) this reverse recovery time.

The MIC2251 data sheet recommends a Schottky diode but points out a fast switching diode can be used (their recommendation is the LS4148, whose trr is less than 8ns).  

See this question for more on diode reverse recovery time.  

A boost converter works by grounding the SW node during the 'on' time, which charges up the inductor.  When the converter switches the internal FET off, the current flowing through the inductor needs to go somewhere, and the diode is preferred.  So the voltage rises until the SW node is a diode drop above the desired output voltage.  When the inductor has dumped its energy into the output cap/load, the diode needs to turn completely off.  While it's turning off, you will get current flowing in the reverse direction, and depending on how long that recovery time is.  The longer it is, the more time there is for current to flow backward and cause heating.  In the worst case, if the switching frequency lines up badly, you can have the FET turning on again before the diode has recovered.  I suspect that is what was happening in your case, since the converter was also exhibiting some temp rise and eventual failure.

You can see a couple examples of the operating frequency and switching waveforms in the graphs on Page 5 of the MIC2251 data sheet.  And there is a graph of operating frequency vs load current on Page 4.