There are three ways to answer this, and they work on different timescales.
By stage. Most stage III and IV sores will be treated by your provider. Ask about any special instructions for home care. Stage III is an open, sunken crater with the tissue below the skin damaged. Stage IV is deep enough to damage muscle and bone. A deep tissue injury — dark purple or maroon, possibly with a blood-filled blister under intact skin — can quickly become a stage III or IV sore.
By time. You may have a non-healing wound if it has not started to heal in 2 weeks, or has not completely healed in 6 weeks. Pressure sores are one of the common types of non-healing wound treated at a wound care center.
Right away. Contact your provider right away if you develop blisters, an open sore, or any signs of infection: a foul odor from the sore, pus coming out of the sore, redness and tenderness around the sore, skin close to the sore that is warm or swollen, or fever. And separately: if your pressure sore changes or a new one forms, tell your provider.
At a wound care center, the team will examine and measure the wound, check the blood flow in the area around it, figure out why it is not healing, and create a treatment plan. The goals include preventing the sore from getting worse or becoming infected, preventing limb loss, preventing new wounds or old ones from coming back, and helping you stay mobile.
Asking for a referral is a reasonable thing to do with these figures in hand. A sore that has not started to heal in two weeks is not a sore that needs more patience.