Is there a "bite" in "respite"?

Over at Language Log, Mark Liberman looks at the eggcorn of the week, from al-Jazeera's website -- rest bite instead of respite:

The skies over the capital have cleared, a welcome rest bite for thousands of people doomed to spend sweltering nights in overheated apartments.

One commenter suggests (plausibly, I think) that "rest bite" could be formed by analogy on "sound bite," to mean a brief period of relief from exertion or hardship. But what surprised me was that the pronunciation with second-syllable stress (res-PITE, ruh-SPITE, ruhs-BITE, whatever) was common enough to produce such an eggcorn.

Yes, I know the variant is out there -- Elster's "Big Book of Beastly Mispronunciations" says it has a "long and tarnished history" -- but I don't think I ever hear respite with second-syllable stress (in "respite care" and the like). Since y'all were so informative (not to mention impassioned) on the pronunciation of often, maybe you could enlighten me about the local renderings of respite you hear, and what you think of them?