There are multiple reasons why a delivery could be stuck in a Pending status. First thing would be can you confirm whether or not this is happening with all recipients or just one, and do you know whether or not the delivery is actually making it to the recipient?
I ask because if the delivery is actually getting to the recipient than it's a reporting issue, which typically indicates a syncing problem where the status isn't being properly reflected on the marketing server.
If it's not getting to the recipient then it could be anything from the delivery needing to be confirmed/approved, the MTAs being down, or a typology or affinity issue which is preventing to delivery from being sent.
I'd recommend reaching out to Campaign Support and providing them with the delivery and recipient information so we can take a closer look.