Yes. Caching is the problem here, as I have found.
To recreate the problem, in Ie on windows, go to Tools|Internet Options|General|Temporary Internet files |Settings
Check for newer versions of stored pages:
If the first one is set, my problem occurs. For the other ones, my problem is gone.
What I see: images disappear, icon in the corner starts rotating, modem sends something, images reappear.
I though that Ie reloaded the images, but now I realise that it only checked for newer versions and then, finding none, loaded the images from cache. I veryfied this by using a very large image and it took the same amount of time to reappear as the small images.
If not, you should still be able to fix this by preloading the image (eg put <img style="position:absolute; left:-2000px;" alt="" src="yourimage"> last in the document)
No, Stefan, unfortunately this doesn't work. I did get my desired behaiviour with using the <img> to go over the <a> (it is the last button on the page), but the buttons above still have their background reloaded.
This is not good.
I know that for me everything will be fixed if I change the options, but there may be many others, who have the same options set as me, or worse, no cache. Therefore, some workaround must be employed for image mouseovers.
I suggest doing what Stefan has said, but for <img> buttons. (It doesn't work with backgrounds)