Would you return your CDP.....

if you turned it on and zero's displayed across the display, you rebooted and it booted up as it should? This has happened to me twice on the past two weeks. I always turn it on and let it completely boot before I turn on my Rogue Cronus Magnum (which I love).
Do you have it plugged into something that's switched?You could check the manual to see if that could cause a problem.If it is the unit and still under warranty,I think I would look in to getting it serviced.They may have a problem getting it to act up though.Hopefully you have a lot of time left on your warranty encase you have to wait for it to get worse.
If defective have it repaired or exchanged. Don't settle for flawed performance even if the issues are minor.

BTW, if it's not a tubed output player, leave it powered up 24/7.
Hifitime. I should have quite a lot more time on the warranty. It's a Rotel RCD-1520 purchased new in July. It sounds great but I'm not totally convinced I like the slot loader.

Audiofeil. It's not tubed so I will take your advice and leave it on. I've never heard a tubed output player before. I would like to hear the difference.

Thank you both for your advice. I've learned so much since I bought my most recent system that if I were purchasing it now, I probably would have looked into other option for a CD player, such as SACD. I have so many CD's thet I really need something like that.