Yes. KIROS expire 13 months after the date your latest purchase is recorded. Each time you make a new purchase and new KIROS are added to your account, the validity period is renewed, so all the KIROS you have earned take a new expiry of 13 months from that latest recording date.
During that time, you can keep earning more KIROS or redeem them for the gifts and rewards available. If 13 months pass with no new purchase recorded and no redemption, the KIROS you have earned will expire and be lost.