I have a circuit that uses an ATTINY84V - the "V" means it works with the voltage as low as 1.8V. I am using all the power saving features possible, so when in sleep mode (which it is in most of the time) it draws only a microamp or so. I am powering it from a 1F 2.5V supercapacitor with a low ESR. (This one: http://www.digikey.co.uk/product-detail/en/B0810-2R5105-R/283-2776-ND/1026744)
I need the supercap to be connected to the circuit permanently, with no on-off switch. I also want it to carry on delivering power as long as possible (in sleep mode).
It mostly works fine. But sometimes the whole thing hangs, and even a hardware reset won't sort it out. Only disconnecting the power (which as I say will not actually be possible in the end product) or reprogramming it (with the supercap still attached) will deal with the problem. This does not happen if the circuit is run from two AA batteries.
I have a feeling that the issue may to do with the way the supercap is charged or possibly discharged. At the moment I am charging it simply by connecting it directly to a 2.5V power supply, via a voltage regulator. There is no current limiter. Do I need one?