One would expect it to depend on skill of the surgeon and any subsequent complications, whether it is in the same uterine horn or the other horn, whether there are single or multiple fetuses and age of the ewe or doe. It is likely that a single surgery would reduce fertility in a measurable way if one had enough observations. And the decline in fertility is probably quadratic rather than linear, decreasing at a greater rate after multiple surgeries.
I am not aware of any published data to answer your question. In cattle, Cesarean sections' affect on fertility is greatly impacted by the conditions under which the surgery is done. Elective C-sections are not expected to be detrimental to fertility if proper surgical technique and asepsis are done. Fertility rates should be interpreted in light of the herd fertility rate. Belgian Blue cows may have elective C-Section done every year of their productive life. Rebreeding is not generally adversely affected. C-sections done under emergency conditions or when fetus is dead are known to have an adverse affect of fertility.