Apart from the shape into which it has been trained, there is no difference between a topiary tree and the same tree growing naturally. The topiary tree requires exactly the same care, but it has special additional requirements.
If a topiary tree has been shaped by the inclusion of wires or lights, the wires need to be checked regularly. The wires must not be able to rub against any part of the tree. If the wires are rusty, you must clean them up. Rust, if present on the wires, will weaken them and also give them a more abrasive surface.
Check Anchor Points
You should attach wires to the topiary tree by anchor points. These will probably be made by fitting steel rods through branches. The nature of these steel rods is varied, but they will include the shanks of bolts or hooks. Make sure the bolt is not rusty and that there are no signs of distress around the hole in the branch.
Some of the branches will be in unnatural positions and it is important that they do not create hollows in which water can gather. This could lead to fungus infections. As the topiary tree will present an unusual profile to the wind, it might suffer damage caused by increased wind resistance. Look for evidence of cracks or splits in the bark.
It is easy to forget that a topiary tree still needs to be reasonably well-balanced if it is going to continue to stand. It is often a matter of checking after each pruning to see that the tree is in balance. If the balance is askew, the tree could start to lean or twist. This movement can be very slow to start with but accelerate rapidly when a critical point has been reached. Adding balance to a tree when an imbalance appears to be developing could involve training new branches into the light area.
Check the Foliage Quality
Make sure that the foliage is still a good healthy green. When foliage starts to fade, it could be a sign that the amount of food production by photosynthesis is no longer adequate. The only answer to this problem is to expose more of the foliage to direct sunlight.
Cut Out Dead Wood
Often, the shaping of the topiary tree leaves some lengths of shoot without leaves. These will often die and look unsightly or even become the site of a fungal infection. It is best to trim these out altogether.
Check for Stability
Many topiary trees have narrow boles and can be shaken mercilessly by high winds. Although the tree will bow with the wind it will also pull at the central rooting system. For trees with shallow roots, this could cause the roots to become exposed to the air. Root exposure is usually accompanied by a weakening of the bond between the tree and the soil. This could, in turn, lead to the tree falling.
Most topiary trees do not have major problems, mainly because of the way in which their design is originally implemented.