Your father might be having an exaggerated GAG reflex, which might be due to many factors such a somatic, psychogenic, congenital or systemic factors. I Need to perform a gag test and determine a gagging score on a D&F gagging index. Once the index score is determined, I can proceed ahead with the right kind of denture material and technique to be used. Since you do not want implants you can go for complete dentures again.
Next Steps
I am a Prosthodontist, practo consult me for more detailed evaluation.
Health Tips
The management of these types of cases are simple but the determination of cause is difficult. Hence i advice you to consult a specialist Prosthodontist.