Electronic – Undeletable EEPROM or other storage for micocontrollers

I don't know exactly what you mean by "stand by operation". You mean sleep? 20 mA is pretty high for sleep. I'd expect less than 100 uA in general.

I'd go with SD card storage. I've designed plenty of "low power systems" and the reality is that most people go to the trouble of going all the way to optimize for low power when in fact it doesn't make that big of an impact (it makes for nice marketing, but marketing doesn't always makes real-world sense). There are many other factors that are more important to logging:

1. Accessibility - An SD card is much easier and faster to read from and access (just take it out, pop in an SD card reader and it's done), and it's faster to do. EEPROM reading requires more equipment. An SD card can be accessed using a file system so it's intuitive

2. Capacity - You won't find anything better than a couple of gigabytes of storage. It's amazing how fast this goes once you start logging.

3. Ease of Implementation - Many commercial and open source applications have used FatFs which you can get for many microcontrollers. It will work nicely. Just open a txt file and save the numbers, one after the other.

An SD card isn't that power hungry. Some have power-down modes after 5 ms that will help.

I can't find a reason not to use an SD card.

It is very simple. Number of pins and cost of packaging.

EEPROM devices are primarily used to store parametric data or characterization constants for a device. The typical scenario is to write very seldom and read typically once each time the host device boots up. For this type of application the relatively slow writing times of EEPROM are of little concern. And the reading time to load at most a few K-bytes of data from a serial device (SPI or I2C) is not normally an excessive time impact.

There is another factor that has played into the popularity of serial devices over parallel devices. That has been the migration of MCU devices from older microprocessor units with parallel busses to the much more prevalent modern types that have all their program storage memory and data memory built right on the chip. Often there is no longer a parallel bus option directly available. And in most applications there is very little interest in using up scads of pins to bit bang to a parallel peripheral.