Chametz As דבר שיש לו מתירין

The Gemarah Pesachim (30a) concludes that chametz is not batal on Pesach. The simple read of the Gemarah is since the law in general is that מין במינו is not batal there is a gezerah on Pesach to say even שלא במינו is not batal. Many Rishonim rule however that is general במין במינו is batal and try to justify the pesak of the Gemarah with the bottom line pesak. 

The approach of the Ramban (Milchamos) is to come with an entire new reason why chametz should not be batel and that is due to the rule of דבר שיש לו מתירין אינו בטל and since the chametz will become mutar after Pesach it is not batal on Pesach. The Ramban asks on himself that there is a Rabbinic issur on chametz not gotten rid of before Pesach, so how is it דשיל"מ if it will not become mutar? He answers the Rabbinic law is meant to serve as a chumrah, not as a קולא to remove the din of דשיל"מ. The Ran asks that this answer doesn't work for the entire din of דשיל"מ is Rabbinic so it has to work within the Rabbinic rules? 

In the post 'After Pesach Chametz' there was a chakirah presented if the issur of chametz after Pesach is an extension of the issur on Pesach itself or a new issur. Rav Leeb Malin (siman 10) says that the Ramban holds the nature of the prohibition of chametz after Pesach is a new issur, not a new prohibition. Hence, the issur on Pesach itself is an issur that is דשיל"מ, there is just a new issur that kicks in after Pesach. This explanation only works if the law of דשיל"מ is a lomdus like the Ran in Nedarim (52a) explains. It if is a simple sevarah to eat something in a state of definitive heter instead of relying on bittul like Rashi Betzah (3a) explains then that should apply no matter what the geder of the issur is. It theory one can explain that is why those that don't like the Ramban saying it is a דשיל"מ. However, since the Ran himself asks on the Ramban, he would have to be asking with the understanding that chametz שעבר עליו הפסח is a continuation of the issur on Pesach.    

The Mordechai Pesachim (תקעג) says that chametz is not a דשיל"מ since it will become prohibited next year. At face value this is difficult to understand, so what it will become assur again in the future, there is plenty of time when one can eat the chametz in a state of heter? The Mordechai would seem to make sense in the understanding of the Ran Nedarim that a דשיל"מ is not batul due to the din of מין במינו in a halachik sense. Since the issue itself will become mutur by itself with the passage of time that proves that the issur is not innate and it is like the heter itself and will not be batal. In light of this the Mordechai may mean that chametz on Pesach is an innate issur, the fact that it becomes mutar after Pesach is not because the issur goes away but rather that the entire shem of the issur is chametz on Pesach and if its not Pesach, there is no issur. The fact that the issur comes back next Pesach in fact proves the issur does not go away but the cheftzah of the issur is tied to the timeframe (in בעניין חמץ בפסח אם הווי דבר שיש לו מתירין footnote 5 he says such an explanation in the name of Rav Shmuel Rozovsky.) [It is noteworthy that the Rema YD 102:4 and clearly R' Akiva Eger understand this Mordechai is a general rule for any issur that will come back again, not just a local severah for chametz on Pesach.]

The Rambam in Maachalos Assuros (15:9) says that chametz is not batal because it is a דבר שיש לו מתירין. According to Rav Leeb Malen that would be because he holds of the lomdus severah in דשיל"מ. The Bach (YD siman 102 #4) proves from the Rambam that even when the food will spoil we still impose the rule of דשיל"מ since the Rambam rules even from the beginning of Pesach the chametz is not batal due to the rule of דשיל"מ even though it will spoil. According to the practical severah of Rashi in that case it should be batal, this would be further proof the Rambam agrees to the Ran. 

The Rambam continues in law 12 יֵרָאֶה לִי, שֶׁאַפִלּוּ דָּבָר שֶׁיֵּשׁ לוֹ מַתִּירִין - אִם נִתְעָרֵב בְּשֶׁאֵינוֹ מִינוֹ, וְלֹא נָתַן טַעַם - מֻתָּר. לֹא יִהְיֶה זֶה שֶׁיֵּשׁ לוֹ מַתִּירִין חָמוּר מִטֶּבֶל, שֶׁהֲרֵי אֶפְשָׁר לְתַקְּנוֹ. וְאַף עַל פִּי כֵן שֶׁלֹּא בְּמִינוֹ בְּנוֹתֵן טַעַם, כְּמוֹ שֶׁבֵּאַרְנוּ. וְאַל תִּתַּמָּהּ עַל חָמֵץ בַּפֶּסַח, שֶׁהַתּוֹרָה אָסְרָה "כָּל מַחְמֶצֶת" (שמות יב, כ); לְפִיכָךְ הֶחְמִירוּ בּוֹ, כְּמוֹ שֶׁבֵּאַרְנ. Achronim ask if the Rambam has a possuk why does he need the Rabbinic reason of דשיל"מ? Presumably the Rambam means the possuk to be an asmachtah to explain why the rule of דשיל"מ applies to chametz even for מין בשאינו מינו. But what does the Rambam see in כל מחמצת that says it shouldn't be batal?