You can be refused homeowners insurance based on your claims history or credit score, or due to underwriting risks such as having a pool, an old roof, or a vicious breed of dog. If you have an active homeowners policy that is canceled for underwriting reasons, then yes, this can impact your ability to get insurance later on.
If coverage is denied because of an unacceptable risk on your property, it could be reinstated if you address the issue. You can also apply to insurers who specialize in helping high-risk homeowners. You’ll likely pay higher rates, but at least you’ll be protected.