Android - SD card readers don't work via USB OTG but USB thumb drives do, any ideas?
I believe that the problem is lack of power. Your phone doesn't deliver enough power to the card reader. I would suggest using the same kind of cable you used to need when connecting an external hard disk using USB. It has one contact for the hard disk (card reader in your case), one for the phone and one for extra power (use a separate USB charger/adapter). That should solve the power problem.
I don't know where one can find this kind of cable in your part of the world. They should be fairly easy to find though.
If this doesn't work I would use the Googles ADB developer tool to check the logs on the phone to see if there are any error messages that could help.