Please post your code so we can check it.
Also what the part number of your meter?
Things I would check:
1) Under the Design Wide Resources -> System, make sure the "Debug Select" setting from "Programming/Debugging" is set to GPIO, and not SWD (SWD draws extra current asynchronously)
2)Make sure you are putting components to sleep as well when your code goes to sleep, as they are all powered/run asynchronously to the CPU
3)TTL pins on the board are generally less lossy when all left at Logic-level-high instead of Logic-level-low (5 volts versus 0 volts)
4)Double check that your DVM is reading/working as it should on another device/resistor if all else fails.
I think your FRAM_I2C custom component is causing the issue. It is better to stop the device before going to sleep mode. Once you are coming out of sleep, you can turn start it. Another factor can be the I2C pins. The GPIOs can continue to drive the external circuitry when the PSoC device is in a low-power mode. This is helpful when you need to hold external logic at a fixed level, but it can lead to wasted power if the pins needlessly source or sink current. So it is better to configure all unused GPIOs to Analog HI-Z unless there is a specific reason to use a different drive mode. Use the _SetDriveMode() API function.
/* Set MyPin to Alg HI-Z for low power. */
This should solve the problem. Please refer this application note while using low power mode : http://www.cypress.com/documentation/application-notes/an86233-psoc-4-low-power-modes-and-power-reduction-techniques
Vasanth R S