Any skipping issues with the Koala tube CD player?

CD players have skipping issues. It's part of their normal operation!
Start from sticking vaccum cleaner tube into the CD-tray hole.
Than you can use lens-cleaning CD with brush.
If two above wouldn't help, you'll need to access your transport mechanizm and clean lens manually with damp cloth and cleaning solution or alcohol
If apperently you find that mechanizm is clean, you should contact manufacturer(hopefully the unit's still on warranty) WTF. CD-players can skip because of DAC failures as well(but substantially more rare).

The skipping started only 2 months after the expiration of 24 months warranty. The lens has been professionally cleaned, the tubes have been changed, the laser-optics has been changed (in strict observation of the written (e-mail) suggestions of the Italian manufacturer, I live in the US), then the CDP has been shipped to the US service shop the manufacturer suggested, and paid $384 for all of these, the CDP came back, it is skipping again. Does this mean the entire transport need to be changed? But I think, changing the entire transport mechanism (Philips/Cosmic L1210) could only be done by the manufacturer, am I right in assuming that?

I was curious reading your post so I did a search for your CD player and got some images. Assuming I was looking at the same player you have, the transport looks very easy to replace. Maybe you can buy the transport and install it yourself.

One other thing you can try is moving the remote far away from the CD player. Sometimes, the remote can break in such a way as to send commands without you pushing any buttons. If the player is getting a false input for something like a seek, you can definitely mistake that for a skip. I thought the transport in my Wadia was going bad when the tray kept opening and closing by itself. It turned out to be the remote.