I followed Google's advice to troubleshoot and try and retrieve my messages. I found there had been suspicious activity on my account from an unknown IP-address (18.104.22.168) which according to the results of an Internet search belongs to the Visto Corporation in Redwood City, CA, USA -- and that, probably as a direct result, my messages had been irretrievably deleted.
ETA: Curiouser and curiouser...
Visto Corporation provides mobile messaging services for mobile operators. It offers Visto Mobile, a platform for mobile service providers to deliver push email, calendar, contacts, and various corporate data to a set of devices; and Visto open solution, which enables email for the mass business market. The company also provides Visto Mobile Internet Edition, which provides mobile push emails for up to five Internet email accounts; Visto Mobile Personal Edition, which is designed for individuals and small groups, offices, and departments with less than five people; and Visto Mobile Enterprise Edition, which is used in larger organizations and allows information technology managers to install..."
Does that sound like they could be spammers? Or are they more likely to be just another link in the chain?