Yes, you can leave an Ayre amp powered all the time. It doesn't hurt anything other than your wallet when the power bill arrives. Sleep mode saves power without powering completely off. I put my AX-5 in sleep mode most nights and I unplug it if I'm gone from the house more than about a week (my previous house was hit by lightning and I lost several components of my then mid-fi system).
I've read accounts of Ayre not sounding its best unless warmed up for many hours. That's not my experience but I rarely go from sleep mode to a full scale listening session, and pretty much never from completely off to critical listening. If I'm home and awake, my system is playing music so it's pretty much warm when I'm ready to sit down and bliss out.