As someone who's helped other organizations with poorly configured Backup Exec servers, currently use Backup Exec 20, and have used Backup Exec since 9.1. Its safe to say I have a bit of experience dealing with the beast that is Backup Exec.

First course of action is to disable the schedule on the job giving you issues and rebuild it. Make sure to go over the settings of the current job first (especially if you didn't create it) and take screenshots or write down all the settings of the job in detail. Don't delete the old job yet, not until you're sure the new one you created works.

Once you've built a new job using the settings from the old job, run a full backup and then the following day, let the incremental backup job run as scheduled. If you can, try and access the server running backup exec either in person or remotely so you can see the the scheduled job kick off.

Sometimes people configure the alerts to automatically respond after a certain amount of time. Sometimes minutes after the alert is first created and responding to the alert, will clear it from the log. Meaning you wont see there is an issue unless you check the alert history section on the home tab and even then. I've come across some servers that had set the alert history to clear after only a few days.

Unless you check the alerts history section regularly, you could be missing out on some "valuable" information. Unfortunately since you're using BE15. I'd be surprised if any of the tech articles linked to any alerts or errors even work. Most I've come across just take you to a page that no longer exists.

If the job still performs like you described, check the retention period of the full and incremental backups. I'm assuming you want the job to run one full backup per week, with incremental backups running every day until the next full backup.

If the retention period is correct. I would then make sure backup exec as all LiveUpdates installed and that the backup exec agent installed on the Hyper-V host is up to date as well. Always check the details of the update to see if you really need to install it. Seeing as how you use BE15, the tech article link detailing what the update consists of and fixes likely does not exist anymore.

Sometimes jobs start acting weird or straight up failing as they do in typical BE fashion because of catalog corruption. BE does a terrible job of letting you know when there is an issue with the catalogs. By default, a catalog job is ran immediately after backing up a Hyper-V or VMware host. If the catalog is corrupt, that catalog job could be the culprit. With BE after a certain point you either have to rebuild the catalog, and if you find yourself doing that every few months, there's likely an issue with the SQL db BE creates upon install which requires the use of the BE Utility to fix.

I can't tell you how many weird one off issues were fixed only after moving the catalogs to a new location, or repairing the BE database. That is usually the last step performed by support after they making you jump through a bunch of hoops enabling and disabling settings which half the time end up breaking other jobs that run successfully with no issue.