How long can we get another fingerprint when first was rejected?

It just really depends on the scheduling with the local office as to when you get called in for a second set of fingerprints.

You must first find out why your first fingerprint was rejected, otherwise subsequent attempts to take your prints will also likely fail. Unless CIS has your fingerprint, it is not likely CIS will approve your case. For some people especially those handling certain chemicals, their fingerprints so degraded that it is not possible to take their prints. If this is your situation, or if there are other unique reasons why your fingerprints are impossible to take, you must notify the ASC officer taking your prints. In such case, a letter from your doctor who can attest to this will also be required.

The government will send you a new appointment.

You may need to go in for another biometrics appointment, and if those prints don't clear, then you may need to obtain police clearance certificates.