I did once. An unenrolled preparer had attempted to help a client by drafting letters for the client to submit. The IRS was limiting the standard deduction of a dependent whose income was earned income from a partnership, treating the income as investment income.
By the time I (EA) received the case, this had been ongoing for some time, perhaps almost a year. I tried resolving it with a POA and I believe two phone calls, but the client continued to receive correspondence. I requested a referral to the TAS. They reviewed the case, one criterion they mentioned specifically was that the time elapsed was sufficient. I gave them our explanation, they scheduled a phone call to discuss progress, and it was solved.
My case was much like Captain's in that the case seemed to have stalled. I would also confirm that the normal channels need to be tried first. If you have a stalled case or IRS personnel do not seem to grasp the issue, I think asking for a referral is very worthwhile.