sqlite & windows: Not enough storage is available to complete this operation and CoInitialize has not been called
The fact this is a transient problem that only happens at peak usage times is a pretty clear indication something is running out of memory - probably your VB DLL (that's likely the only place where CoInitialize is being called).
I've seen similar problems with too many applications running and winDoze running out of "system handles" - I've got a w2K Advanced Server box I've been using as a desktop machine (because m$ doesn't provide an upgrade path from an AS instance to a desktop one) typically running a dozen Explorer windows, WinSCP with 8-10 tabs, several PuTTY sessions, several DOS boxes, remote desktop connections, Firefox with 184 tabs in 4 windows, Thunderbird watching 40 email accounts, WinAmp, and a few others - and PaintShopPro and PhpED just do not want to be running at the same time due to the aforementioned system handle limitation.
Your problems might be fixed simply by throwing more RAM at the issue, but you should probably do some performance checking, and check for system settings to tweak.