How do I write off an unpaid balance to my vendors?

Accounts Payable is not normally written off, unless you never received the service or product. It is also not normally written off, should you pass the terms. Failing to pay for services or products could be considered a tort claim.

That being said, here are the two options you have-

1) If you are writing off an agreed upon amount, i.e., issuing a debit memo, the transaction (and there are several ways it can be done, based on your industry):

Accounts Payable    $xxx.xx

                Original Expense/Asset Account used $xxx.xx

2) If however you have no intention of paying, and you received the goods and/or services, the transaction would be:

Accounts Payable    $xxx.xx

                Other Income        $xxx.xx