coming out from underneath. So I took some roofing cement and with a
putty knife managed to cover the nails under the shingles in the spot
of the leak. Last night I went to check for leaks during the rainstorm
we had, so far no leaks.
But has anyone ever heard of this problem? Why are the edges sealed in
the first place?

They're sealed to keep the lower edge from lifting in the wind,
but they're supposed to be held down with just a dot of glue
on each tab, not a continuous bead.