I have had 14 picture books published and 100+ work-for-hire elementary texts. All my books were well-reviewed and most sold moderately. Despite this, I have been turned down by every single agent I have contacted. My theory is that they don't want to represent a writer who doesn't illustrate because their percentage of the five percent royalty is not worth their time.I can't guess (with this amount of information) why you're being turned down for representation, but I can assure you that it's not because you don't illustrate. Lots and lots of picture book writers who only write are repped by agents. It may be that the books you're writing are consistently niche-market enough that some agents may not feel your advances are large enough to be worth their time, but it may also be that you haven't submitted to enough agents. Submit, submit, submit!