We have had a slow leak for 20 years. The roof has been replaced. We still have the leak, so how do we find the leak?
The source of the leak could be a penetration of some sort. If you have roof vents, sky light, chimney, etc.. there could be opportunity for water to get in. I have had trouble with the same thing and have found several places to look. Stack boots around the vents.. Older ones are metal with sealant around the opening. newer ones are plastic with a rubber seal. This seal dries out and cracks. Check the flashing around chimneys and skylights. Flashing is made of metal and can fatigue or corrode if bent causing cracks to form. Some flashing is embedded in masonry when the chimney is built, other flashing is sealed to it with tar or caulk. I have roof vents to cool the attic and have found out they were not installed correctly. The shingles on the low side were put down on top of the flange and not under it. Check all of these places for bad seals. I sealed as many of these places as I could find and have gotten most of the leaks.
If it is a flat roof, it may have a drain on it. This drain can clog or fracture causing water to find alternate routs. If water backs up on a flat roof (new or old) chances are, you will get a leak.
Also keep in mind, leaks travel. you may have water dripping out of an area in the middle of the roof, but the entry point could be several feet away.
This is a long shot but.., possibly, if the roof is over a single story of a two story house (like an added on family room), there could be a leak in the plumbing from an upstairs bathroom finding a path to the roof and showing up as the leak.
Particularly if the roof is a flat roof, it is possible that there is still water retained within the roof structure.
When that happens, it could take months for the water to finally dry out. If this is the case, you will notice that water will still emerge regardless of the weather conditions - the rate of water escape will be almost constant (in terms of it not leaking more when it rains), but will gradually decrease over a period of time until the retained water has finally escaped.
One option to test a flat roof is to block the outlet, flood the roof to an appropriate level, and monitor the water level over a period of time to see if it drops. If it doesn't drop, the leak is fixed.