When a rubber roof starts leaking it can be a real hassle to get it fixed. Sometimes you can't find the leak, sometimes you fix the hole but it doesn't fix the leak... it can be frustrating, time consuming, and costly. Here are a few tips and suggestions for your project to (hopefully) take away a lot of the stress and cost.
The first thing that you must realize is that rubber roofs are often done in layers. Often when a roof is replaced the old rubber won't be removed; a new layer will simply be put on over the old one. Eventually the entire thing will have to be torn off so as to avoid too much weight, but before that you can sometimes end up with two or three layers of rubber on top of your roof. So what's the significance of this? Well, just because the ceiling is leaking in one room doesn't mean that the actual leak is directly overhead. More often than not, the actual leak is located slightly away from the ceiling leak, and the water is running between layers to find a course to an old injury or puncture. Just because you can't find a hole doesn't mean that one isn't up there somewhere, especially if the ceiling leak is in or near a location that's leaked before.
When looking at your roof, be sure to prod various sections that look questionable with a stick or pole before stepping onto them. This will help you to find weak sections (which are a good indicator that the leak is close by, since it's likely water damage that's weakened them), as well as to help avoid both injury and further damage to the roof. The last thing you want is to step onto a section of the roof and have it give way beneath your weight.
To help identify the source of a leak, it's best to start by investigating any places that look like they may be damaged or warped. If you can find a crack or hole there, then you may be in luck and have found the only damaged point, but it's still advisable to keep looking.
After the initial spots that catch your attention, start looking at any places that look wet even though the surrounding roof is dry, or any places that are exceedingly dirty (the dirt will collect in the places where water is standing, which may be where it's entering the roof.) Also focus hard attention on any pipes, vents, or fittings that come out of the roof, as even a small tear near one of them can take water to all parts of the roof.
Once you've located the areas where you think the damage has occurred, it's time to fix the hole. Be sure to clean the area with benzene cleaner or other rubber cleaner, and apply a liberal amount of roofing cement. Be sure to overlap the rubber patch well over the hole, taking your time to make sure that there are no air bubbles under the rubber and that there is a good seal on all sides. If you're patching around a vent, pipe, or wall, you need to make sure to go up the sides slightly and get a good seal. For round pipes, there are commercially-available rubber pieces that will fit over the pipe and surround it as one piece (thus getting rid of a potential leak at a seam); just be sure that it is well-cemented.
After you've patched your roof, wait several days or until the next time that it rains. Keep an eye out for any leaks or further water damage, and check the roof afterwards for any rubber that may not have been well sealed and thus has pulled away or blown loose.
Should you still have problems with a leak, you can try patching the roof again, or you might want to consider contacting a roofing contractor to see about getting the roof professionally patched or replaced.