I agree a properly equipped trailer should be able to handle rough roads. However after encountering many miles of rough roads, it might seem reasonable that some maintenance might be needed.
This posters experiences on these very rough highways stands to reason that suspension components and axles, wheels have developed some wear/fatigue, or need some adjustment .
While the OP reports the trailer not being overweight. Many miles of SEVERE bouncing, with a trailer loaded up to capacity, could have as much the same effect as being overloaded.