My question relates to Security Clearance Renewals.
What happens if your losing organization does not want to renew your Security Clearance simply because you are leaving? Will it impact the search for jobs on this site or impact your eligibility.
Some service member may lose their security clearance simply because they are leaving the force.
Are you talking about a military service member?
They could still require a clearance if they are staying in the reserves.
Yes. However, this military service member is not joining the reserves.
Well, one could say they found a reserve unit 
Sometimes even the specialty (AFSC, MOS, rating, etc) requires a clearance.
DoD normally does not “renew” your clearance if you are one year or less from retirement or separation.
Many companies are HAPPY to hire vets and run them through the clearance process. A good FSO may be able to speed the process and an interim is a possibility because of the recent cleared work.
Others can address this far better than I.