No, you should not keep asking someone about their sexuality if they deny it or express discomfort with the questioning. Respect for personal boundaries and privacy is essential in any interaction, and discussing one's sexuality is a highly personal matter.
Sexuality is a deeply personal aspect of a person's identity, and everyone has the right to disclose or not disclose this information as they see fit. Pushing someone to admit something they are not ready to share can be invasive, hurtful, and disrespectful.
If someone chooses not to share their sexuality with you, it's important to respect their decision and give them the space and privacy they need. If they feel comfortable sharing that aspect of themselves with you at some point in the future, they will do so on their terms.
Remember, the most important thing is to be supportive and accepting of others, regardless of their sexual orientation. Let people be themselves and respect their autonomy in deciding what they want to share with you or others. If someone does decide to open up about their sexuality, be understanding and supportive without judgment.