The answer to this question is a bit complicated and depends on the situation. If you are asking if permission to contact expires once you have made initial contact with someone, then the answer is generally no. However, there are some exceptions to this rule. If you are asking if permission to contact expires after you have received a response from the person you contacted, then the answer is yes, permission generally expires at that point.
There are a few different scenarios in which permission to contact may expire once initial contact is made. For example, if you are trying to reach someone who has unlisted their phone number or changed their email address, your permission to contact them may expire after one unsuccessful attempt. Additionally, if you are contacting someone for a job or other professional opportunity and they have already told you that they are not interested, your permission to contact them probably expires at that point as well.
Generally speaking, though, if you have been given permission to contact someone, that permission does not expire until the person tells you explicitly that they do not want to be contacted anymore. So long as the person has not asked you specifically to stop contacting them, it is generally assumed that they are still open to hearing from you.