A quick update.

I've been in touch with our hosting service's tech support this evening.

They informed me that they weren't able to find any errors in their logs with our site. I provided them a sample of email notifications I received from the site when it was unable to connect to the database or otherwise experiencing database issues. They then told me that the site is scheduled to be migrated to a new, better equipped server (with SSDs) in the immediate future and were fully prepared to do it tonight if I wanted. I told them to minimize impact on everyone using the site to schedule it for Friday, Saturday, or Sunday overnight. As of now the migration will take place Sunday.

I haven't been provided any details on what this will entail or what is needed from me but I will be sure to get it taken care of. The site may be offline for a bit at this time. I'll be doing a full backup Saturday just in case.