Hi Ruud,
How long long do you want to keep the clock running for?
I originally designed my 5V only imx28 board to use a NiMh battery to keep the internal rtc alive (Re: i.MX28 RTC Backup Battery Connection ) but in the end I switched to use an external rtc with super cap.
There are a few issues trying to keep the clock alive:
1) the keep alive current is large compared to RTC ICs
2) the voltage must be above 3.1V according to the data sheet to keep the clocks running so you only have 3.3 to 3.1V drop. In practice I found it to work down to around 2.5V but I don't like designing off-datasheet
3) using the 24MHz crystal clock for the imx28 is not particularly accurate. Especially as it needs to be placed next to the imx28 which gets warm under 5V only operation due to the internal LDO so your run-time accuracy may be tens of minutes out per month
Using an external rtc I could charge my super cap to 5V, the RTC runs down to approx 2V and only takes 1uA. I could also place it away from warm components but I am now switching to a TCXO to ensure accuracy of <10 mins error per year.
I am not sure you will achieve much better than minutes of keep alive directly with the imx28. I would expect the 24MHz keep alive to be much worse than 32.768kHz too.
One more thing to check - are you charging your super cap through a schottky? If so check its reverse leakage as some of the low vf schottkys have terrible reverse current that may be helping to drain your battery back via your charging supply!
Mark