The remedy that lasts the longest is a complete re-install/upgrade of the same version that's running. Since I'm hosting this VM in the Amazon cloud, it was fairly painless to update the machine to a more powerful VM. Strangely, the problem still happens in about the same amount of time.
I've read some anecdotal reports of similar issues caused by the size of the disk write buffers in the VM coupled with the somewhat slow speed of the Amazon EBS volumes. If the buffer size is based on a percentage of total RAM, larger instances try to flush much larger chunks of data less often. I'm no expert on this stuff, but perhaps someone on this list has had similar experiences?