Publishing problems with web host Easily

Does anyone else here use a web host called Easily, based in the UK? I am having terrible problems with missing files — usually individual images, sometimes whole pages. What happens is that when I publish a new page from Sparkle, or an amended page, something else is wiped off the server. Duncan has suggested that I ask them to turn off the server-side cache, which I have done, but they keep ignoring my request and telling me it is a coding problem, which is illogical. Any fellow sufferers out there?