We did an injection weekly for the first 4 weeks and then monthly after that, personally I noticed improvement by the 3rd weekly injection apart from my boy who was getting them for severely arthritic knees..his improvement was a lot quicker. But usually by the end of the weekly injections they (the ones getting them for IC) had almost all stopped squeaking. I did have one who, after the weekly injections had to have one on week 3 instead of waiting the month, but after that, she was fine monthly.
It did help I think that my vet showed me how to do them myself at home, so they didn't have the stress of going to the vet every time which may have sped up the effectiveness of the injections.