What you need is a technique called wear leveling. It doesn't write your data every time at the same location in the EEPROM, but uses some algorithm to use different locations. I've read about complex wear leveling algorithms, but I wouldn't know why the following simple method wouldn't work.
Add to your data a 24-bit counter, so that your data block is for instance 8 bytes long. Pages on a 24AA64 are 32 bytes long, so a 64kb EEPROM holds 256 pages. From the datasheet:
"When doing a write of less than 32 bytes
the data in the rest of the page is refreshed
along with the data bytes being written.
This will force the entire page to endure a
write cycle, for this reason endurance is
specified per page."
so it doesn't make sense to use data blocks smaller than a 32 bytes page.
Look at the counter of the first page. If it's zero you used the maximum number of write cycles for that page, so you move on to the next page and check that counter. Repeat until you find a counter > zero. That's the page you're currently using. Microchip's EEPROMs have a 1 million cycles endurance, which you can increase to 256 million with the given example of maximum 32 bytes per block in a 64kb EEPROM. That should be enough to outlast your product: 40 years if you write once every 5 seconds(!).
You'll want to initialize your EEPROM on first use. How do you know when that is. Use the last page to write a unique signature upon initialization. Check at each power-up if the signature is there. If it isn't the device has to be initialized. You can preset the counter in each page with 0xF4240 (for 1 million) or clear everything to 0xFF and write the 0xF4240 when you first use the page.
Initializing an EEPROM is needed because sometimes a certain pattern is written to it in the production/test process.
edit
The wear leveling should solve your problems, but I still want to comment on the capacitor solution. You say the board is rather power-hungry, but maybe you can isolate the microcontroller/EEPROM's power from the rest of the board with a diode. So you'll probably need only a few mA when main power is gone. The 24AA64 writes a page in less than 5ms, then at 10mA and an allowable voltage drop of 100mV you'll need
\$ C = \dfrac{I \cdot t}{\Delta V} = \dfrac{10mA \cdot 5ms}{100mV} = 500\mu F \$
Easy with a small supercap.
further reading
datasheet 24AA64
EEPROM Endurance Tutorial
From what I can see, the (main) difference between it and SRAM is it's slower, and the difference between it and EEPROM is it's more expensive.
I'd say it's sort of "in between" both.
Being a pretty new technology, I'd expect the price to drop a fair bit over the next year or so providing it becomes popular enough. Even though it's not as fast as SRAM, the speed is not bad at all, and should suit many applications fine - I can see a 60ns access time option on Farnell (compared with a low of 3.4ns with SRAM)
This reminds me - I ordered some Ramtron F-RAM samples quite a while back, still not got round to trying them yet...
Best Answer
All STM32 MCUs have self-programmable flash memory. If you need to store user settings, you can store them in an area of flash.
ST provides a library to perform EEPROM emulation on the STM32F4. (There are similar libraries for most of their other parts as well.) Even if you don't plan on using that library, their application note explaining how it works may be interesting to read.