You may see three different problems, if you have a slow connection to the e-tamago server in Japan. The best way to avoid this is to use e-tamago when all of the Tamagotchis in Japan are asleep. When I am in North America I often see #1 and #2, and rarely #3. When I am in Japan, I rarely see #1, and almost never see #2 or #3.
#1. While you are navigating between pages, you may see a blinking picture of Mametchi driving a blue race car. This screen means "please wait a moment". Usually, after a moment, either the new page will finish loading, or one of the below two problems will occur.
#2. If your tamagotchi character gets "stuck" between locations within e-tamago, hit your browser's Refresh button (or the F5 key if you're using Microsoft Internet Explorer). This will take you back to the login password entry page. Re-enter the same login password, then immediately go to whichever location you got stuck going to before.
#3. When you are navigating between pages, your progress may halt at a picture of Mametchi, Memetchi, and Kuchipatchi stuck in space between Earth and the Tamagotchi home planet. This screen occurs when there is a load error. There are two buttons above the Earth. The red button means "retry". The blue button means "stop". If you press stop, you will be taken back to the first page (before the login screen).