I'm still baffled by 'stopped trigger'. Trigger can be disabled, or invalid. Use the USER_TRIGGERS view to inspect the state of the triggers.
In the USER_OBJECT view, there is the LAST_DDL_TIME column, but I don't thing that trigger invalidation or disabling would be reflected there. It could be still useful, though (perhaps the trigger was modified by someone).
If the trigger just does not do what is expected from it, it looks like there is a bug in it?
(Also, it is best not to use triggers at all. Triggers can give rise to very nasty and complicated bugs, most often when someone forgets about the magic done by the trigger behind the scenes. If a trigger can be replaced by a stored procedure, that would always be a better approach. Just saying. )
Check the status of the triggers as Martin suggests. It's possible that your DDL might have invalidated the trigger, if the trigger was referring to the column you changed, but it should have sorted itself out afterwards:
Compiled triggers have dependencies. They become invalid if a depended-on object, such as a stored subprogram invoked from the trigger body, is modified. Triggers that are invalidated for dependency reasons are recompiled when next invoked.