How common is it for journal to reject a solicited paper? A guest editor at a peer-reviewed academic journal solicited me to write a paper. I initially hesitated for lack of time. But the editor's invitation was courteous. So I sent an abstract, which was accepted by the editor.

I submitted the 6k-word paper a few weeks later, taking care to comply to the submission guidelines (I downloaded the journal's CSL file for bibliographic references, for example).

I just received a rejection letter. I know an invitation is not a ticket to bypass the reviewers. Still, I am rather stunned. I'll get over it, but I was wondering how common it is for academic journals to reject solicited papers?
This is not common, but it certainly does happen.  I know a small number of people who have had their invited submissions rejected.  Whether it is a likely possibility in particular instance will depend on how many invitations the editor(s) send out—and, correspondingly, how well they know the potential contributors and their work.  If the invitations are kept to a relatively small group of individuals familiar to the editor, it is less likely that anyone will submit a manuscript that is of low quality or is not topical.

Whether this is likely to happen also depends on how the submissions are being evaluated.  Sometimes, an expert guest editor for a special issue may take care of all the refereeing themself.  However, this will not work if the topic is too broad or there are too many submission.  I was actually responsible for getting a low-quality invited paper rejected from a special issue once, when I was asked to referee it.  The work was simply too shoddy to merit publication in any venue.