STM32F103 Systick Interrupt stopped working when debugging in ram - (Coocox IDE)
You need to relocate the vector table — right now, the processor is probably still using the copy of the vector table in FLASH, which will point into an old version of your code in FLASH. (Or, if you've erased FLASH since you started developing in SRAM, the vector table in use will be blank.)

If you're using the STM32 Standard Peripheral Library (SPL), you can define the VECT_TAB_SRAM macro to have it set the appropriate flags to use a vector table in SRAM. If you're going the bare-metal route, you need to set the TBLOFF field of VTOR to point to the base of SRAM (0x02000000 on STM32F1).