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Message expiry can be reset for played messages only: Log into your account online (voicemail.its.utexas.edu), select message(s) to be reset and click the Re-save icon.
Note for subscribers who forward their voice messages to email: Depending on the volume of messages you receive, your mailbox could eventually reach full capacity (disk quota is about 200 minutes of messages) and stop taking messages. To prevent that, log into UTVM periodically (perhaps monthly or weekly depending on your usage) and delete messages.
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