He was then diagnosed with cancer in January and passed away by the end of February.
Is it possible the life insurance company would not pay out on his life insurance policy due to it having been not even 6 months since starting up the coverage??
It's possible the insurance carrier may deny the claim if there was any reason to suspect that he may have a pre-existing health condition that he didn't disclose when he applied for the life insurance policy.
Some life insurance policies only pay out if all medical questions where answered fully and correctly at the time the coverage was purchased.
So, if your father wasn't well and had some tests taken prior to taking out the life insurance policy, AND he didn't disclose those tests or their results to the insurance company, yes, they can deny the claim on the grounds of a pre existing illness (not covered) or deceit (he knew he was sick but withheld the knowledge). This would be considered a material misrepresentation on the application for coverage.
The life insurance company has 2 years from the time the policy is issued to contest the coverage and deny a claim based on material misrepresentation. So, if he died within 2 years of buying the life insurance, and he lied on the application for coverage, and that lie was information about a health issue that was not disclosed, the life insurance company may choose not to pay the claim based on this situation.
However, you may want to speak with your life insurance agent, the insurance company, or a legal advisor with experience in life insurance contracts to get a better understanding of the handling of your father's life insurance coverage.