Need help with SD Card Initialization (CLK Syncronization)
Your diagrams show chip select as always active. I do not say that it would not work this way, but deactivating CS, in most of the cases, signals card that host is finished with the command.

The I have the following suggestion for you - change the way you access the card:


when powered on, you must clock CLK for some time (70 times or something like this) to enable card to initialize and synchronize;
when you want to access the card, you have CS as high (inactive), and perform 8 spare clock cycles to the card. MOSI stays high;
then you get CS low, and perform another 8 spare clock pulses with MOSI being high;
starting next clock cycle you shift command into the sd-card. After command is shifted in, you wait for response as instructed in the documentation;
after you have got required response, you do NOT deactivate CS, and perform 8 spare clocks with MOSI high;
then you deactivate CS, and perform another 8 spare clocks with CS high and MOSI high.
and then you are ready for next access.