I'm not sure there is any primary functionality in Unity Connection or its APIs to implement this functionality directly, especially the 'retry until they acknowledge' aspect.
A few thoughts:
If the user's mobile device is running Jabber/Webex client (e.g. via MRA or VPN), then I believe they would get mobile OS notifications for the voicemails (if configured/enabled). Not as attention-grabbing as a repeated incoming voice call, but users typically do pay attention to phone notifications
If not, you could use Webex messaging, SMS, some other messaging client, or build your own notification mobile app to provide notifications that there are unread urgent emails. This would require a service monitoring user mailboxes via the Unity Connection Messaging/Notification Interfaces (CUMI/CUNI), sending outbound messages somehow, then updating the mailbox/message (again via CUMI) to mark the message as read
If you really want repeated voice calls made until the user listens/acknowledges, you should be able to implement something like that by adding CUCM CTI function (via TAPI or JTAPI). Your service would do something like:
Monitor mailbox incoming message events via CUMI/CUNI
Download the message audio via CUMI
Use TAPI/JTAPI to place an outbound call to the mobile phone
Use TAPI/JTAPI CTI Port media playback capabilities to play out a greeting then the message audio
Use TAPI/JTAPI DTMF events to interact with the user (press X to mark read, press Y to delete the message, Z to forward, etc.)
Use CUMI to manipulate the message, e.g. mark it read/delete/forward
Similar to the above but simpler, perhaps the CTI app could call the user, play a greeting 'You have urgent voice messages, please hold to be connected to your voice mail box', then use CTI to redirect the outbound call to the mobile to the target Unity Connection mailbox DN. Assuming the user listens-to/disposes-of the message via normal Unity Connection DTMF interaction, your app would receive an event via CUMI/CUNI to that effect and could stop repeating the voice calls.