From the Guidelines

The risk of vasectomy failure in preventing pregnancy is approximately one in 2,000 after a man has achieved postvasectomy azoospermia.

Vasectomy is not 100% reliable in preventing pregnancy, even after vas occlusion is confirmed by post-vasectomy semen analysis (PVSA) 1.
The time to azoospermia varies widely, but by 12 weeks after the vasectomy, 80% of men have azoospermia, and almost all others have rare nonmotile sperm 1.
Postvasectomy semen analysis should be performed 8–16 weeks after a vasectomy to ensure the procedure was successful, and patients should abstain from sexual intercourse or use barrier methods until they have confirmation of vasectomy success 1.
The risk of pregnancy after vasectomy is approximately one in 2,000 for men who have post-vasectomy azoospermia or PVSA showing rare non-motile sperm (RNMS) 1.

Vasectomy is intended to be a permanent form of contraception, and patients should be counseled about the permanency of sterilization and the availability of highly effective, long-acting, reversible methods of contraception for women 1.
Male sterilization does not protect against STDs, and consistent and correct use of male latex condoms reduces the risk for STDs, including HIV 1.

From the Research

The risk of vasectomy failure in preventing pregnancy is a critical consideration for individuals opting for this form of male sterilization.

The failure rate of vasectomy is less than 1% in most reported series 2.
Vasectomy is 30 times less likely to fail than its gynecologic counterpart, tubal ligation 3.
The European Association of Urology (EAU) recommends an ejaculate analysis 3 months after the procedure to confirm sterility, which helps in identifying potential failures early on 4.
Complications such as vasectomy failure due to recanalization are relatively rare but must be considered 4.

Several factors can influence the failure rates of vasectomy, including:

Technique used: Certain techniques, such as fascial interposition, seem to decrease rates of vasectomy failure 3.
Surgeon's experience: The skill and experience of the surgeon performing the vasectomy can impact the success rate of the procedure 4.
Postoperative care: Adherence to postoperative instructions and follow-up care can help minimize the risk of complications, including failure 5, 4.

While vasectomy is considered a safe and effective method of permanent contraception, long-term considerations must be taken into account:

The possibility of vasectomy failure and the need for alternative contraception until sterility is confirmed 2.
The potential for long-term complications, such as chronic pain syndrome, although rare 5.
The option for refertilization, which is successful in about 90% of cases with experienced surgeons 4.