Hi Liz,

Do the outstanding transactions have a current balance other than zero? If so, they will not be cleared until they are applied to something and have the current amount set to zero. It is not enough for transactions (invoices, cash, credit notes, etc) to net to zero; they must have zero current amounts individually.

If the transactions are all still Current, then you need to create a zero dollar cash entry for the customer, then apply to all invoices and cash so that the net of zero still occurs. Posting this entry will not generate any GL activity and now these transactions will be able to be cleared to history via Day End (or printing statements, whatever you do).

Purging from History is a different matter - transactions do not need anything special other than an old enough date. You should be able to run the Clear History function and remove Historical Transactions for all or particular customers.

If the problem is offsetting transactions, you can also use the Create Write-off Batch function under Maintenance. Ask it to writeoff Balances between -.01 and .01. It will create a batch of adjustments.
Looking at the batch you will see each positive transaction followed by a negative one for the same amount. Unless you have some whose balances were .01, the total of the batch will be zero.
You can edit the batch to delete anything you do not want to include, then post it.