Yes, definitely! See there is not limit or restriction on either your age or the number of attempts in National Eligibility cum Entrance Test or NEET like in some other examinations such as JEE Main. So, it absolutely does not matter if you have failed your class XIth examinations.

As far as you have a valid certificate which states that you have qualified your class XIIth examinations, you may give NEET as you want.

Hope I have answered your question. All the best!