Do EEPROMs lose their data over time?
Yes, they are based on a stupidly tiny charge on a floating gate, so eventually they will lose their memory.
The time is generally pretty long under benign conditions (seldom, if ever, re-written, cool temperatures, no significant ionizing radiation).

If any of those things are not true, the life can be significantly foreshortened. For example, at high temperatures rule of thumb is half for every 10°C (not sure this is 100% valid for EEPROM cells, but let's use it here).. so that 100  years becomes 50  years at 35°C, 25 years at 45°C, 12.5 years at 55°C and so on.. so at the maximum storage temperature of 150°C the retention might be less than a week.
Similarly, a badly written or errant program can quickly exceed the lifetime 10^6 erase/write cycles in a matter of hours.
I believe there is some interaction between the two- many write cycles negatively impact the retention time.