Well I don't know what plastic you are working with, but my guesses are that it is a thermosetting polymer. Basically, picture polymers as chains of molecules that are weakly bonded. In some cases, heating the plastic will push the molecules to create hard covalent bonds between themselves called crosslinks, which causes these plastics to irreversibly harden. You will not be able to melt it, or even reshape it.

Usually polymers go through a glass transition at a certain temperature (called, surprise, surprise, the glass transition temperature). Below that they are hard and rigid (like glass), above that they become rubbery. Smaller molecules, called plasticisers, can be added which will artificially decrease the glass transition temperature (e.g. PVC tubing compared to uPVC used in windows and doors). Since these are small molecules they are more volatile and once gone, the polymer will become glassy (those PVC tubes stiffening with age). So my guess would be that the plasticisers in the bag have evaporated, causing the polymer to transition from rubber to glass despite the increase in temperature.

Thank you! So if I understand correctly, once it is at this glass state, it can become rubber if heat is continuously applied or is this glass state permanent? Hopefully I’m understanding this process correctly

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Yes, while it is above the glass transition temperature it will be rubbery and become glassy again when it cools.

Thank you so much :)

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Standard lightweight plastic grocery bags are generally low density polyethylene, which has a glass transition temperature well below room temperature without plasticizers. What's more likely to be happening is some combination of crystallization and thermal breakdown of the polymer.