No, your total number of Status Points will always be the total earned in the previous 12 months. When you upgrade, you maintain the Status Points earned and can build on these to further upgrade.
If you spend 6000 Riyals per month, you will earn 60 Status Points per month.
After two months, you will have 120 Status Points and will upgrade to Silver
After five months, you will have 300 Status Points and will upgrade to Gold.
Gold is valid for 12 months, so 12 months after upgrading to Gold, you will have earned 720 Status Points in the preceding 12 months (60 per month x 12 months), so your Gold status will be renewed for another year.