I was told that the exchange sets a conversion factor that remains fixed during the futures contract "life". However the exchange fixes the factor for simplicity, altough it varies.
The conversion factors published by the exchanges relate to the bonds that are deliverable to the underlying future.
The conversion factor is fixed for a given bond in the deliverable basket for the life of a given futures contract. The conversion factor doesn't change. If you think about what the conversion factor is and how it is computed, you'll realize that it has to remain constant for each given bond/contract combination.
Yes, the conversion factor is the easy part if it is in the deliverable basket (see attached spreadsheet). Computing the repo, carry, etc is usually the hard part for illiquid issues.