I think it depends on the kind of oil.
I make infused coconut oil and keep it in the freezer and haven’t had a problem. I store it stick form similar to butter, individually wrapped in cellophane then put in a freezer bag. If want to cook with it or make canna caps I take a stick out and defrost it.
I found this online:
Coconut oil is very stable and depending on the kind, can last anywhere from 18 months to several years. Opinions differ on how long cannabis-infused oil can be kept. Most agree that degradation begins after 2-3 months, and sooner after repeated exposure to air (opening and shutting the jar) or overexposure to sunlight or heat. This does not mean it is unusable, but you will definitely start to notice a change in the taste and effectiveness as the cannabinoids begin to degrade.
If it’s an olive or vegetable oil it’s my understanding that 10 days to 2 weeks is the max in the fridge before you risk bacteria as it’s not as stable as coconut oil. Not sure how accurate that is but when I googled it that what came back.