LTC3525 Shutdown feature reacts to wrong thresholds
Wrong assumptions and interpretation of datasheet specs.


  SHDN Threshold Voltage 0.4 Vmin, 0.6 Vtyp,  1 Vmax    


This means it switches On OR Off at some threshold of 0.6V with a worst case tolerance of +0.4/-0.2V. ( Disabled active low or negative logic)

When they define a logic level, for safety margin from noise they define a "1" above some level and a "0" below some level. "1">=1.0V and "0"&lt;=0.4V but it has  some real threshold that is variable in between.  

So SHDN should not be used as an accurate Ultracap charge comparator.

It does not mean what you said... "This is not as it should be, because the LTC3525 should disconnect the output when V_SHDN is less then 0.4V and reconnects when more than 1V."

The other board switches OFF and ON @ 0.7V so this is close to typical.

You need a better comparator to control SHDN.