SD-CARD reads first few files correctly, then the remaining wrong!

Have you verified that all of the SD-CARD files are able to be read successfully all of the time when using a PC with a proven card reader to access the data?

Have you tried a different SD-CARD to see if another unit works differently than the first?

Have you tried running the SD-CARD I/O at a different clock rate?

I wouldn't trust the SD-CARD itself completely until it is well verified to behave properly in different readers.

If you find that the SD-CARD itself is likely OK then you could check to see if design or implementation errors may be responsible for the problems -- check the configuration parameters regarding the design, check that there are no service packs for your synthesis tools that are missing and which may be responsible for causing the design to be incorrectly implemented.

Also verify that the board is getting properly stable / regulated voltages and that none of the components seem to have been damaged by ESD or other situation.