To solve the immediate problem:
Open the Vendor list, locate that Vendor, edit it, click on the Transactions tab, double-click on the specific invoice transactions, then set the "Maximum payment" amount to the remaining balance.

To reduce the likelihood of future problems:
Open the Company Profile, click on the System Options tab and put a check-mark on "Set Amt Payable to Inv balance".

Note: This is the same as Support's response but I'll leave it up anyway.