...But you don't have to take my word for it.
'Reading Rainbow' Reaches Its Final Chapter : NPR
I wonder how many kids actually still watched this show in recent years. I know I hadn't seen it in a long time, at least 15 years. This is the theme song I remember, but I remember seeing a newer one online a couple years back.
To summarize the linked article: it appears that the show just lost funding. They mention some changes to the US Department of Education under Bush and I guess compounded with the financial situation the US is in it trickled down to this.
If I had access to PBS, I would watch that last episode today.