Unless I'm missing something why would you need to add that field if it's automatically created?

Need to see your code.  
It sounds like you are setting the Account Number (unique key) outside of your append loop instead of as a part of your append loop.
In other words you need to DMax + 1 for each record that you are appending.  Saving as you append a record.

Alex, the field is not automatically created.  I don't know of a way to do something like dmax(("acctno","cust_t")+1) as a Default Value.  That would solve the problem, but Access does not recognize the DMAX statement in a default.  Any idea around that?

As for Scott's inquiry.  There isn't any kind of loop set up.  It is simply an update in mass.

Gerald - -
A regular append query will not work in your case, as you found out.  The DMax + 1 in the criteria field sets all of the records to that value.  It isn't applied for each record.

When the field you are updating is unique (and I'm assuming required??) you have to go at it in a different method.
Do a search of loops.  I see you have Developer 16.  A Record Set loop would be preferable depending how many records you have.

HI Gerald, DMax+1 can only add one row, because in an append query all rows are added in one go, not one at time -- so DMax+1 can only work for the first row.  DMax has no awareness of each row being added individually, and that's why DMax+1 doesn't work here.  If you want to add N rows with DMax+1, you either have to make N separate append queries, or use VBA to add each row separately.

The ability for a query to process each row individually is called "transactional" ability, and Access doesn't have that.  But SQL Server does.  In SQL Server, an append query can indeed do what you want.

Sequential Numbers

Why does it need to be sequential?