Can Shanghai residence permit and social security be renewed after 3 months of suspension?

No, pension insurance and medical insurance are cumulative payment years and can be interrupted. I don't know whether you pay social security by yourself or at work. If you pay your own money, it will mainly affect the medical insurance benefits, and there will be a waiting period. If the payment is stopped and continues, from the second month after the payment of the basic medical insurance premium, you can use the funds in your personal medical account and continue to pay the basic medical insurance premium for six months, and you can enjoy the basic medical insurance benefits such as hospitalization reimbursement as stipulated in the Measures for the Basic Medical Insurance of Urban Workers in this Municipality.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.