Also, you need to make sure the mcu won't attempt to write into EEPROM until the big cap is fully charged - most of the time this is fulfilled but with short pulses on the AC mains you might get into trouble.
This apply to power-up an is totally irrelevant, When the supervisor drop the reset there is no problem writing.

An another thing, you need to make sure that the peripherals won't "suck out" the "big cap" too early - even if they are not connected directly to the . Beware, this behaviour can/will change depending on their state and the connected "outer word".
two solutions
a) set them "low power" on the power down int
b) supply only the uC an memory from the "big cap"

I did not say this can not be done, as I don't say the IRAM backup cannot be done (in powerdown mode). My point is, that each of these is not completely trivial and you need to consider carefully all the circumstances of your particular application.
I have done it several times and have yet to actually have calculated the "big cap". You can back up all you need in a millisecond and to hold enough for the 7805 to function for ONR millisecond + a power cycle (10 or 8 ms) is no big deal.

The voltage drop will be the same a (ripple on the "big cap" *2) if you take 10 ms to back up at 50 Hz (bridge recitified).

Jan, you are making a mountain out of a molehill.

Erik

The real caveat: If you try to be fancy and do something like a "machine shutdown cycle" or such all Jans reservations apply. What I discuss is keeping power for the few milliseconds it takes to move a few bytes to an EEPROM.