It was repeatedly found that when speakers produced a word, such as “lion”, they were slowed by a constant amount of time for each previously produced word from the same semantic category, for example the words “elephant” or “zebra”. That is, there was a linear relationship between the ordinal position of a category exemplar in the experimental list and the naming latency. This cumulative semantic interference effect observed in the context of the continuous picture naming task is the main motivation for adaptive models of word production. Notably, all studies reporting this effect have examined the interference only across five (or six in one case) ordinal positions. We investigated whether this linear increase would continue when testing more ordinal positions – namely, ten or fifteen. Inconsistent with the predictions of current adaptive models, but consistent with evidence from the learning literature, we found that the increase in the interference was restricted. Additionally, we found that the interference decreased with a long lag (introducing unrelated naming episodes) and that its developmental trajectory was similar before and after the lag. These findings require an adjustment to existing adaptive models of word production.