Payment terms of 1% 10, net 30 days - our system deducts the discount when checks are issued within the 10-day time, and mailed the same day. Our vendor is not honoring the discount because they didn't receive our payments within the 10-day time. Is this correct?

Your agreement with them should address the 10 day. 10 from payment/mailing or rec'd by 10 days. We don't know the terms of your agreement.

Their intrepretation would be the commercial norm.