The assessment instructions will tell you how long your assessment responses will be reused for that assessment.
If you apply to another job announcement and see a prompt to take a USA Hire assessment (i.e., Assessments are Required notification), then your reuse period has ended.
A note about similar assessments
There are many types of USA Hire assessments, some tailored for specific agency or job needs. Even if a new assessment looks similar to one you've already taken, it is different if you are prompted to take it again within your reuse period.