Daedric Shrine problems...

You do have the appropriate Soul Gems in your inventory, right?

Maybe the spell has worn off by the time you kill them

Well one, get empty soul gems, and two you could use Umbra's sword to soul trap creatures to make it alot easier.
-Salex

In the hermaeous Mora quest you need to capture 1 soul of the 10 different races in cyrodill, he gives you a spell to trap those souls, if you are unable to trap a sould perhaps the spell wore off or you have already collected a soul of that race.

Yes. You do not need a soul gem for this quest. It is an exception, all you need to do is cast the spell hermeaus mora gave you on the target, make sure that it is working and is the right one, and kill the targets. Preferrably, go aroud to each daidric shrine and kill the inhabitants, as it will help you get the souls, and they arent important anymore, and you wont notice they are gone.

Use umbra's sowrd and make sure to have plenty of empty soul gems.

For one, Hermaeus Mora gives you his own soul gem and soul trap spell. If you think you need your own, you're mistaken. And make sure you only cast the spell on ONE person at a time and KILL THAT PERSON before you do that soul trap spell on someone else. If you FAIL to do it that way, it will GLITCH you out of that part of the mission, and you wont be able to do it. So I highly suggest saving it right after you get everything from him, and going to all of the other Daedra Shrines and killing the worshippers. All 10 races are DEFINATELY within the area of them. There is only 1 High Elf out of all 10 Daedra Shrines, so be careful...and make sure you go for him first. And I don't understand why people are saying you need your own soul gems and Umbra's Sword. Umbra's sword does NOT have the correct soul trap. (Hermaeus Mor's Soul Trap spell is One-of-a-Kind.) And he definately gives you his own soul gem for you to give him when you are finished. No wonder some of these people are having trouble with this mission. They don't pay attention to the top of their screens long enough to realize that they have what they need already. But PLEASE only cast the spell on one person at a time until that person has been killed. We don't want any more Attention Span of a Fish Comments, here.