According to the Illinois DOR:
As a nonresident, you must file Form IL-1040 and Schedule NR if
- you earned enough taxable income from Illinois sources to have a tax liability (i.e., your Illinois base income from Schedule NR, Step 5, Line 46, is greater than your Illinois exemption allowance on Schedule NR, Step 5, Line 50), or
- you want a refund of any Illinois Income Tax withheld in error. You must attach a letter of explanation from your employer.
http://www.revenue.state.il.us/Individuals/FilingRequirements/
If your business trips are for a "a temporary or transitory purpose," you are still considered a nonresident.
