Didn't see your second post there for a bit...
I had four problem areas while I was trying to get this to run. The first was getting the clock to tick at all. The second was with the synchronization between the RTC domain registers and the APB1 registers. The third was getting the global interrupt to be generated and the fourth was with the EXTI interrupt.
Yes, it works fine for me on a Maple Mini using the LSI clock.
If nothing works, my guess is that the synchronization is not working. You need clocks running on both sides of the interface for things to work properly. See section 2 of app note AN2821 (google 'stm32 AN2821') for the full list, but the brief summary is APB1 clocks for PWR and BKP domains as well as the RTC clock. If it come out of the rtc_init() routine, all this should have been done. It will hang on rtc_wait_sync() and or rtc_wait_finished() if the clocks are not there.
Since the RTC runs when the MPU is completely shut down, there is a fair bit of complexity in the intertface between the two.
To debug, stick with the LSI clock. It's got to be there. Look at the CRL register for the RTOFF and RSF flags to come up. Watch for the seconds count register to increment. If you get that operational you are in good shape.
You said you have an Olimexino board (nice looking board, BTW. Like the SD card). Hopefully you are not having a $(BOARD) problem. You have other LeafLabs example programs running, right?