Which webmail, classic or enhanced? If classic, are you using the graphics editor? What OS and browser are you using? Enhanced webmail uses flash and the graphics editor uses Java, either could cause problems. I don't believe the graphics editor even works with current versions of Java. Are your plugins up to date?
So, As stated before, Cox is aware of the problem with Classic Webmail and is working on it, I'm sure it will be fixed in the near future, but for those who simply must have their E-mail right now, fear not, there is a quick and simply work around that solves the problem most of the time.
Log into your Classic Webmail as normal, then if you see the 500 Servlet Error popup, then simply go up to the address bar and you should see something like "webmail.east.cox.net" Now just replace the word "East" with "West" and then, press ENTER. You should then see the screen reload and then you will be able to access you email.
At that point you can either bookmark your Classic webmail this way or just swap EAST & WEST when you log into your Classic Webmail, until Cox has the issue resolved in the next few days.