The datacenter is reporting that they're still waiting for all of the new switching equipment to arrive before the old can be replaced. I've been with this company for 10 years and I've never been so disappointed with them.
The good news is that we've worked out a (possible) temporary solution, which should prevent the site from being knocked entirely offline every few minutes. I have applied these changes to the server now; please let me know if you continue experiencing problems.
EDIT: According to the bandwidth graphs, the issue is still there, though these changes may have fixed the frequency and length of the outages.