Is it true that if I earn a certain amount above proverty level my disabled daughter can lose her social security benefits? She is about to start school and am a single parent about to get a promotion which means more money and would like to know how this may affect my disabled daughter's social security.

A quote: "If your child's income and resources, or the income and resources of family members living in the child's household, are more than the amount allowed, we will deny the child's application for SSI payments."
See: Benefits For Children With Disabilities (http://www.ssa.gov/pubs/10026.html)

Yes, it can be based on income ability

Benefits For Children With Disabilities (http://www.ssa.gov/pubs/10026.html#ssi-benefits)