There is a possibility that dc from the LD's output is triggering the protection circuitry in your power amp.
Basically, when you switch on the Little Dot the output caps will need time to charge up, until then they will pass dc voltage which will very likely damage your speakers/headphones, the caps are there to block it and just allow ac through.
A directly coupled amp has no capacitors in the signal path, so some manufacturers fit protection to prevent damage, this may be the cause of your trouble.
Did you allow the LD to warm up for a few minutes beforehand?