http://www.swtire.com/ptiretips.html
Does the wear look like any of these?
http://www.shorelandr.com/pages/o_tirewear.html
Are the brakes locking up and causing the wheels to skid?
It seems odd that you are experiencing this problem after you had the trailer, but the previous owners did not.
There are numbers on the inside of the tire that indicate the date of manufacture, I'd check them to see how old they are. We had a blowout running on tires that were over 5 years old. They looked brand new, but they were the original tires. When we had the blowout we replaced both tires on the trailer (the dealer only had 2) and then later replaced the spare.