This seems to be a regular issue for a lot of people. It is surprising that nobody has come up with a solution yet. The fact that Apple doesn't even address the issue anywhere is very telling.
This has happened to me on my 4s, 5 and 5s phones. It happened with the apple alarm and with third party apps. I have replaced my alarm app at least 4 times over the past couple of years trying to solve this. I even purchased an alarm app to try to resolve it, but this morning, it happened again.
I did not update my software yesterday, and I have done nothing different with my phone since the last time. I woke up 20 minutes late and saw the alarm was going off silently. I raised the volume- nothing. I flipped the silent switch (I am ALWAYS on silent)- nothing. I tried a test with a later alarm (preset), still no luck. And this is all on a 3rd party paid alarm app.
Later, I changed the time on one of my preset alarms for another test, and it worked. It seems that the solution is to reset my alarms on a regular basis. The iphone gets bored with the same old alarms and you have to take it out to dinner and spice things up every now and then before it will put out.