The best you can do is just follow the thread in the server alerts section. Server maintenance is far from easy or predictable. I'd say within the hour, but things tend to get worse before they get better when you have 10,000 hosting accounts on one server :D
You would need to find or create a script designed to back up your site. You need to set it up with CRON using CPanel -> Advanced -> Cron Jobs. You give it an interval and the absolute path to your script and it will run every period you specify.
Unfortunately, another user discovered the same problem with their account today. There is nothing that can be done. X10 does inform you when you sign up that because free servers are subject to very high levels of abusive use, you should back up your own data. The R1soft backup is really a last...
I have google apps and provide google apps accounts to a few of my website members and honestly, I thought I would be using it all the time. But, there are so many efficient ways of sharing data otherwise, I haven't used it once.
I don't care what validation you use, that website is BAD!
It almost looks like someone completely colorblind and mostly blind in general created it in the early 90's as an experiment to see if websites can cause seizures in epileptic individuals, paid for 200 years of hosting service, and then...
You could use CRON to backup your site in the future.
On the free servers, people sign up for accounts and do abusive things with them that crash the servers. We catch them and remove their accounts, but users like you suffer because of other's dumb actions.
I'll escalate this issue to staff so they can take care of it. I've never heard of this issue before, but it does make sense that it would cause problems.
Hm. Try using the R1soft recovery tool in your CPanel. See if there is a backup just before the reboot. The reboot may have caused some data loss, though I haven't heard of any problems from anyone else.
Unfortunately, if that doesn't work, you have to do it all over again.