We handle our down message at the load balancer, which works well for us. If this is an option in your organization perhaps it is worth pursuing instead of your current approach.
That being said, the process of unpacking, modifying, repacking and deploying analytics.war and analytics.ear is quite easy to mess up, especially if you don't do it often or this is your first attempt. So in your case you are trying to add some <error-page> tags to web.xml.
1) Can you check your deployed web.xml file and confirm your changes are actually there? Your deployed web.xml file is going to be in some directory like this: ORACLE_HOME/user_projects/domains/bifoundation_domain/servers/bi_server1/tmp/_WL_user/analytics_11.1.1/7dezjl/war/WEB-INF/web.xml
2) Assuming you know where your deployed web.xml sits on your server and you do in fact see your changes, then you might try pulling up F12 in Chrome (developer tools, check "preserve log" option) or whichever browser you use and see if your browser attempts to go to your custom maintenance page at all. That could give you some more information on what to look into.
Thank you for your answer.
Our customer doesn't use load balancing, so its not an option.
With the information you provided, I was able to understand what was wrong with the steps I took :
After deploying the analytics.ear, I should have stop then start the services. That's when the ear is actually deployed.
Again, thank you for your answer.