Why would a switching power supply fail with a battery supply?
The LT3988 data sheet mentions the use of ceramic capacitors at the input: 


  A final caution is in order regarding the use of ceramic 
  capacitors at the input. A ceramic input capacitor can 
  combine with stray inductance to form a resonant tank 
  circuit. If power is applied quickly (for example by plugging 
  the circuit into a live power source), this tank can ring, 
  doubling the input voltage and damaging the LT3988. The 
  solution is to either clamp the input voltage or dampen the 
  tank circuit by adding a lossy capacitor in parallel with the 
  ceramic capacitor. For details, see Application Note 88.


You might want to add some extra input impedance to your source.