cheaper tires are made from cheaper soft rubber which does not hold the bead as well. ALSO some SLIME (a gooey green gross slimy substance you can put in your tire) can also help with small leaks on the bead, small punctures too.
http://www.slime.com/
All the guys I ride with swear by a can of it per ATV tire and they barely ever have to deal with tire issues. So I followed suit and no tire issues since installing it.
BUT when you need to change or take a tire in for patch it will cost you extra to have tire fixed as they have to clean all that crap off the tire before they can patch it and it is gross to deal with.
BUT a side note hard riding in wet still firm clay is VERY hard on ANY ATV tire though.