I have a alarm clock with SSD1306 OLED. The init code is kept as long as the OLED has power, but I turn off the content after some seconds. At the moment uptime is >200 days from two AAA cells. Controller is a STM32L031, which is in deep power down mode (only RTC runs) for most of the time.
I think the most important trick is to use a step up converter. I use the XC9142 to generate the 3.3V from the two AAA cells as long as voltage is above 0.7V. This means, your hardware will run until your battery is really empty (<0.4V for one 1.5 AAA cell).
Oliver