There are two issues that may be causing the issues with your chimney stack, firstly it may be a pointing issue, the second could be the flashing that surrounds the chimney stack. If the pointing is still intact, then it is very likely that the flashing has decayed. This is the sheet of metal that joins the roof to the chimney, which can cause the chimney to not be watertight. One of the most common issues with chimney stacks is the natural erosion of the pointing.
It is visible when the jointing between the course of stonework is no longer meeting with brickwork, it will be noticed that this is what the chimney is breaking away. Before the erosion took place the mortar mix would hold the courses together, if there is an almost black void, this will indicate a problem and this will need to be rectified. If these problems continue and are ignored entirely, they will certainly fasten the problems and result in more severe structural issues.
An important part of re-pointing your chimney stacks is maintaining them, if water was to seep into your chimney this can cause a considerable amount of damage that can require extensive repairs. No one wants their chimney to suddenly come crashing down, so it is crucial that your chimney stacks are properly maintained.