Thanks for this. I have sent you the log by email, as you suggested.
Re your reply, I'm not sure what you meant by "did you set up the app to sync on WiFi (or mobile) connectivity changes?" In the app settings, under "Mail, Receiving, Scheduled checks" I have checked "Use WiiFi only, scheduled checks." That's it. I don't see a setting for "sync on WiFi connectivity changes."
Also, I should add now that it seems to reload deleted emails no only when I turn off WiFi and turn it back on again, but also when the phone's been recharged, when I changed the debug log settings, and on various other occasions, such as when I go into another app (like messaging) and then come back to Aquamail.