This BLOG began last daf yomi cycle in October 2006 with Beitzah. Rather than reposting what I had written then, I will post the link and try to build on it.
Based on what I wrote above, the logic of Rashi should be limited to food which can only be eaten once, but would not include hana'ah which can happen multiple times (tzlach), and the logic of the Ran should be limited to ta'aroves and not apply to a safeik (which the tzlach also say). Therefore, something which is an issur hana'ah that can be used multiple times, and is a safeik rather than a ta'aroves, should not be considered a davar sheyesh lo matirin according to Rashi or the Ran (assuming the tzlach's sevara is correct).
The Tzlach also writes that if we are forbidding an egg that is layed on yom tov and gets mixed with others based on davar sheyesh lo matirin, it should only be assur to eat, but should be mutar to move because tiltul is like hana'ah. However, according to Rav Yehuda who holds of muktzah (to the exclusion of Rav Shimon), since they are forbidden to eat, all the eggs become muktzah and cannot be moved either.
In my shiur this morning I was asked, what if the food will spoil by the end of shabbos or yom tov, would we still consider it a דבר שיש לו מתירין? It would seem clear that the sevara of Rashi doesn't apply, but the sevara of the Ran would still apply.
Returning to the approach of the tzlach, I think that there is a serious difficulty based on the gemara 4b. The gemara asks about a branch which falls into an oven and one is then mevatel using heter wood, that it should not be batul since it is a davar sheyesh lo matirin. The gemara answers that since the issur is destroyed and not intact, there is no issue of davar sheyesh lo matirin. The difficulty is that even without the answer of the gemara, it should not be a davar sheyesh lo matirin. We are speaking about wood which is used for cooking. Certainly that wood can be used multiple times and the cooking after yom tov in no way precludes the ability to cook on yom tov as well. So, why does the gemara consider it to be a davar sheyesh lo matirin, since it can be used multiple times, it should be considered ein lo matirin. This seems to be a pretty strong question against the Tzlach!