In general peach trees are susceptible to insect and disease issues and generally require a spray schedule for control. They are not long lived trees.
Peach trees can exude sap/gum due to any type of stress such as pruning cuts, wounds, cankers, or possible insect pests such as the peach tree borer in the trunk or lesser peach tree borer in branches. These are two similar pests that attack different parts of peach trees. The borers enter the lower trunk around the soil line and feed on the cambium. They push out a mixture of frass and sap, which can be scraped away to expose the feeding tunnels. There are no chemical controls.
Cankers can enlarge and girdle limbs and trees. The fungus usually invades dead or weakened wood and can go into healthy wood. There are no chemical controls. In general, Peach trees should not be pruned before March. Make sure all dead wood and cankers on small limbs are removed. Avoid excessive fertilization.
Keep the tree in good health through proper pruning, planting, watering, and pest management. Keep a ring of mulch around the base of the tree to conserve moisture and keep weeds down. Make sure mulch is not thicker than two inches and keep away from the base of the trunk.
For more information on anticipating and preventing problems see our publication on stone fruits http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG77_IPM_Series_Ston...
and our fruit Profile on Peaches