ATtiny85 doesn't work with E2-library

I want to use an ATtiny85 to pick up signals from several air quality sensors, do some arithmetic and send the results through one wire to a controller-unit. I succeeded in talking to a DHT22 humudity and temperature sensor, but the communication with an EE893 CO2-sensor using the E2.h and E2.ccp libraries fails. On an ATmega328 it works perfectly well.
I set my ATtiny to 8 Mhz and I varied the delay factor to make the bus work, but whatever factor the sensor gives 0.00. Sometimes, mysteriously, at startup the sensor gives a good result over the tiny85, but it hangs on the same value.
Is there anyone who has an ideas about what is going on?

Try tuning the oscillator.

Try running the t85 at 16 MHz.

I just got some information from the supplier of the CO2-sensor. The bus speed should be less than 20 KHz. Is that possible using an ATtiny85?

I can't think of any reason it would not be possible.