I use a tube preamplifier and tube power amplifiers, but have only powered down my CD deck less than a dozen times in the past decade (when system changes/maintenance were performed).
Not familiar with your player, but mine has so many power supplies I figured it's best to keep it powered up 7/24/365 (and it's performed w/o a hitch since purchased in 2001, or so).
I also keep our Sharp mini system powered up 7/24/365 as it takes 3-4 days (from a cold start) to sound half way normal (a week plus is more like it).
Both the CAL/CD and the Sharp/Mini draw very little current @ idle (unoticable on our power bill) so I consider these little crosses OK as we do conserve energy use in many other ways, on a whole.
Leave the CD deck powered up for a week and see if you notice an overall difference/improvement in the sound quality.