PS. We just finished a job a few months ago that was a 4/12 slope. They had about 6 leaks. All in wide open areas of the roof. We took off the existing shinlges and installed GAF Rubberoid Mop Grade. Not a Drop Since! :)
I get the same thing sometimes. One thing you can do if its a 2/12 or better is cover the entire area with ice and water shield and then shingle over it offseting your shingles at least a foot apart if its dimensionals ( this wont help if its 3-tabs as the maximum you can get is 6 inches due to the water being able to enter at the key ways ) The leaks occur on these low slopes by water running horizontally under the shinlges where they butt together if its dimensionals and in the keys and the butts with 3-tabs. ( Its much harder for the water to travel a foot than 6 inches or so.) If their is a slight unlevelness its worse and the water can reach the butt and get under the shinlges from there. It can happen around nail heads also but this is not as common. Also you can go back and seal every nail head and every butt joint with plastic roof cement ( underneath the shingle ). This is a pain in the arse so i guess it depends on how bad you want the job. I also see this problem sometimes on 4/12 to 6/12 slopes as well. The key is a smooth deck surface. So If the levelness of the deck is questionable then you can deck over with plywood or osb to give the maximum levelness. My experience has been that if the deck is almost perfectly level and all other things near perfect as well there is never a problem. Using dimensionals instead of 3-tabs is a big advantage also. Of course there is always the 4 inch exposure as well instead of 5 inch. If its under a 3/12 on one of my jobs its getting shingle grain surfaced modified rubber, period ,regardless of what the home owner wants. If they wont listen to me then so be it. Sometimes your better off passing on a job rather than have a problem a year or two later on down the road. So don't worry yourself to death about "losing" this job. In reality the only thing you may have lost is a huge problem.
Manufacturer's do warrantee it.
Check their specs on line.
3/12 isn't flat.
Manuf. won't warrantee shingles on flat.
To them, flat = less than 2/12