Check your broadband connection with this link:
http://www.pcpitstop.com/internet/pinger.asp
Just to see what kind of numbers you're getting.
Anyway, when I ping 208.245.147.9 I get a request timed out. In fact, if I ping interactive brokers hoempage I get a request timed out. But I haven't had TWS go down in a long time. I only go down, when everyone goes down which is signalled here:
http://www.interactivebrokers.com/en/software/systemStatus.php?ib_entity=llc
So if you don't see a red flag on that page, it means the problem is somewhere between your computer and your ISP.
Also, uncheck SSL and see if it's stable. If it is, then the IP your ISP assigned you doesn't work well with IB's SSL. The solution to that is if you have a router which allows you to clone a mac addy. Clone the mac addy of your computer. The mac addy the router defaults to is the one of your cable modem. If you have any nic card laying around that you don't use, close those if your computer mac addy doesn't work. Cloning the mac addy gives you a new IP from your ISP. Remember to reset everything (computer, cable modem, router) after cloning in order for it to work.
Also, try reinstalling the Sun Java. It can get corrupted by adware/spyware/trojans. Then reinstall TWS.
But before all that run a virus check of your system. Here's a link to a great online virus scanner.:
www.bitdefender.com
and... If TWS goes down, log onto webtrader. In fact bookmark webtrader's URL login screen.
Best of luck to you.