Every music genre, whether it's metal, progressive rock or electronic music, some songs are 20-30 min long, you turn your player off and next day, you either start from the beginning of last song again, or simply go to next song.But why not start, where you left off?????
I know I'm fighting losing battle here, but I can't understand why can't this feature be included in any cd player?????
DVD and Bluray players have memory buffers - think of it as computer RAM. The data is read off the disc and written into the memory. This is where some processing is done - the type of processing is dependent on the type of product. The data is then read from the memory and forwarded to whatever circuit is necessary to complete the task - be it video, audio, data, whatever.
A DVD or a Bluray player will have a larger memory buffer and this memory will be kept under voltage even if the device has been powered down. Remember that most of these devices have a standby mode which means at least some of the electronics inside are always powered on. With DVD and Bluray players, this typically includes the memory buffer circuit. Hence, the information remains stored even if the player is turned off.
CD players either have no memory buffer or use it for a different purpose. For instance, CD players intended for professional use will have memory buffers to prevent the CD from skipping. This is called 'anti-shock' memory.
That being said, some portable CD players, namely more high-end Sony ones, have had the resume feature and so did the MiniDisc players. The machine would 'remember' the exact position of the laser even if it was powered off. However, the memory would be wiped if you removed the battery.
That doesn't answer your question why CD players don't have this feature. In many cases, designers believe that simpler is better. I never gave it a second thought till you asked the question and I have loved CDs for as long as I can remember. Symphonic parts can be 20 minutes long and I've never found it necessary to stop playback, turn the player off and continue the next day. In worse case scenarios, I've fallen asleep to the music and listened to the piece from the start the next day.
I don't think a CD player needs that particular feauture but I hope I've shed at least some light on the topic for you.

Cheers - Antun