填 that ,这是固定语法需求
She said that ...
I found that ...
We agreed that ...
都是固定的结构
They found that things are often famous for only a short time
that 是连词,引导宾语从句 that thing are often famous for only a short time
其他类似例句：
She said that I was late
I found that some food can actually harm you
We agreed that we would meet again tomorrow
我把原句改通顺一点,另外,这样说更地道：
They have found that fame often lasts only a very short time.
他们发现,声誉很常是昙花一现