Low Disk Space Alert plug-in question

I'm seeing odd activity with one of my accounts using the Low Disk Space Alert plugin.

A week ago I received a series of 'low disk space alert' emails (27 within one hour), stating "There is currently only 0 megs free". There had been no updates made to the website or in CMSB during this time and there was plenty of space on the server and database.

At the same time, the site went completely offline and an error message was displayed. I forgot to note the error message, but it mentioned the plugin and space. A couple of hours later, the hosting company replied, confirming that the database was not even near being full and that the site was back online, but that they had not made any changes. (They're usually forthcoming with any errors on their part, so I believe them.)

Then for the past couple of days, I've received batches of 'Low disk space alert' emails (4 within 1/2 hour one day & 16 within 1 hour another day). I haven't noticed the site offline these last two times.

All three of the email batches were sent at different times of day, so there's no pattern there.

This is a shared hosting server, but the database is not shared. Perhaps a process on the server is conflicting with the plugin? What questions should I be asking my hosting service?

is conflicting with the plugin? What questions should I be asking my hosting service?