can a job hire you have you work for almost 2 months then terminate because of your background

I worked for a company they asked about my background I was honested and said a domestic back in 2011 so they hired me still had me working for a month n a half I quit my two wks in there because it was to much gas for my truck so couple days latter they called me to come back for more money so that's when i worked a month n a half then they called an hr before I had to go to work and told me not come in because i was termanited because of my background