Once a can is opened, it needs to be treated with the same care you would provide your own food. Serve the wet food at a time of day when your cat is likely to consume all or most of the food in a reasonable period of time. You're doing the right thing by putting the unused portion of food in the refrigerator to keep the food from spoiling. However, even though the food is being kept refrigerated some bacteria could be being produced that may be causing the vomiting. It appears that storing the food for 12 days may be too lengthy; you may want to not store the food for more than 4-5 days. This may require offering slightly more food or purchasing a smaller can of wet cat food. You will also want to warm it up to at least room temperature before serving.