@Jeruba Assuming my guess about the underlying cause is correct: servers are like any other computer, which means they slow down if they are constantly processing information and never getting reset/restarted. But unlike most computers, servers need to stay running all the time so that the websites they host are always available. There’s a finite number of operations a computer can perform before they are running so slowly that they cannot process information fast enough to avoid timing out (basically, a safety valve that says “you’ve been running this process too long, abandon it before you crash”).
There’s various ways of mitigating this in between resets, one being to assign priorities to different processes. Decorative graphics are not essential to making a site function, so they tend to be given a lower priority. This is why losing the graphics is an early sign that the servers need to be reset. While the other processes are running normally because they have the normal amount of processing power assigned to them, graphics go missing because they are the first process to get shortchanged when there’s not enough processing power to go around.
With apologies to John Powell, whose explanation would have certainly been better, clearer, and much funnier.