This question came up again (Living in Florida working remotely - NY employer withholds NYS taxes - Correct or Incorrect?) and the poster on the new version didn't find the existing answers to be adequate, so I'm adding a new answer.
NYS will tax this income if the arrangement is for the convenience of the employee. If the arrangement is necessary to complete the work, then you should have no NYS tax.
New York state taxes all New York-source salary and wage income of nonresident employees when the arrangement is for convenience rather than by necessity (Laws of New York, § 601(e), 20 NYCRR 132.18).
Similar text can also be found here: http://www.koscpa.com/newsletter-article/state-tax-consequences-telecommuting/
The NYS tax document governing this situation seems to be TSB-M-06(5)I. I looked at this page from NYS that was mentioned in the answer by @littleadv. That language does at first glance seem to lead to a different answer, but the ruling in the tax memo seems to say that if you're out of state only for your convenience then the services were performed in NYS for NYS tax purpose. From the memo:
However, any allowance claimed for days worked outside New York State must be based upon the performance of services which of necessity, as distinguished from convenience, obligate the employee to out-of- state duties in the service of his employer.