score:3
Yes, you can - of sorts.
When you redeem the voucher you will need to mail it to AA (or take it to an airport location). After it is processed, they will mail you a new paper voucher for the remaining value (presuming it is more than $5).
This process normally takes (at least) a few weeks, so there will be a window where you will not be able to use the remaining credit, but when it is issued the new visa will have a 1 year expiry.