Some of the reasons a fixed bridge will not be recommended for a patient are the following:
Lack of bone to support the missing tooth or teeth, if you do not have ample bone on your anchor teeth to support the missing tooth, you can lose those anchor teeth also!
Also, if the bridge is a long-span bridge, missing many teeth, and even though the bone around the supporting teeth is good, you can lose the anchor teeth, or cause mobility once the porcelain bridge is constructed, due to your bite and occlusion.
If the patient wishes to floss each individual tooth and does not want to use a bridge threader to clean underneath.
If there is one missing tooth, and the teeth next to the missing tooth are healthy and no large filling on them, it is best to preserve the tooth structure and simply do an implant (implant can have their own contraindication also).