There are occasional reports of a toenail not growing; however, in most instances, the nail is growing, it is just doing so so very slowly that it's difficult to tell. Nails grow slowly: it will take an average of six months for a fingernail to grow out completely, and a toenail takes at least twice as long. They also seem to grow more slowly as we get older. Sometimes the cure is simply patience. If you just wait, eventually you will see growth.
In other instances, the appearance of a toenail not growing may result from it being worn down or destroyed so fast at the tip that no growth is visible. Sometimes activities (like a daily walk, barefoot on a sandy beach?) Will wear away the tips of the nails so that they never have to be cut, much like a dog's toenails will be kept short by walking or running on pavement all the time . Infectious causes could be at work as well. Fungal infections of the nails often make nails soft and crumbly, so that they come apart and remain short. Infected nails are usually yellowish or brownish, thick, distorted and unhealthy looking. An antifungal treatment of some kind is needed to resolve this kind of problem.
When you truly have a toenail not growing, it could be that the root of the nail is damaged. The root is hidden under the flesh at the base of the nail, between the cuticle and the knuckle. Specialized cells here pack together dead skin cells into dense layers to form the nail. As the cells in the root pack together more and more skin cells, the ones that are already packed are pushed outwards. If, for any reason, the packing of cells stops, the nail will stop growing. There could be various reasons for this, ranging from physical damage to the root, to drug side effects, or disease processes. When there is no obvious history of finger or nail injury to explain a toenail not growing, a doctor should be consulted.
To have a toenail not growing is a rare thing. Unless there is something obviously wrong with the toe (indicated by swelling, inflammation, pain, discoloration, etc.), there is probably not a problem. Wait and see if a month changes your perspective. The nail will probably have inched forward a bit by that time.