There is no limit of Attempts. As per the eligibility you should not be more than 25 years as a General Category & 30 years as a reserved category.

You are required to complete 17 years of age either at the time of admission or else on or before December 31, 2019. You can check teh further eligibility with the given below link.

https://medicine.careers360.com/articles/neet-eligibility-criteria

Good Luck!