The OLED driver circuit needs a small amount of time to be ready after initial power. If your code tries to write to the display too soon, it may not be ready. It will work on reset since that typically does not cycle power. If you are having this issue, try adding a small amount of delay before trying to write to the OLED.

In Arduino, use delay() to add a few milliseconds before calling oled.begin(). Adjust the amount of delay as needed to see how little you can get away with for your specific setup.

The display can have image burn in for any pixels left on over a long period of time - many days. Try to avoid having the display on constantly for that length of time.