Should You Leave An External Power Supply On 24-7?

yes

I just got a response from the Teddy Pardo company saying that it should be left on all the time because it does not use very much power and that the unit does not get warm.

Yes my SS equipment is on 24-7 330 days a year. 

I power down when I go on vacation. 

I have an LTA linear power supply.  LTA told me to leave it on 24/7.

Yes my SS equipment is on 24-7 330 days a year.  I power down when I go on vacation. 

+1 @jacobsdad2000 That’s what most solid state manufacturers seem to recommend (including Pardo, who knows better about your PS than anyone here).  I left my solid state components on (except for extended vacations) and had decades of trouble-free performance.  Plus, leaving something on means it’s always warmed up and ready to play, so there’s that nice little bonus.  Just my $0.02 FWIW.