(Sorry, I see "dmertz" already adressed this... anyway, my reply gives the code support for that answer)
I do not think the "taxable earnings" requirement applicable for traditional and Roth IRA's is likewise applicable for SEP-IRA contributions, see IRC 408(k)(8)(B), 414(s)(1), 415(c)(3)(B):
"(B)Special rule for self-employed individuals: In the case of an employee within the meaning of section 401(c)(1), subparagraph (A) shall be applied by substituting “the participant’s earned income (within the meaning of section 401(c)(2) but determined without regard to any exclusion under section 911)” for “compensation of the participant from the employer”.
