My old cable company (Adelphia) was the same way for a long time...really pissed me off sometimes.
Since I moved in January I've been using SBC ADSL and the consistency just rocks...bandwidth doesn't fluctuate, ping is always low, I'm always able to connect, and I never get disconnected. The only drawback in your case is the low bandwidth, which is probably fine for web browsing, but not so great for big downloads. It may not have great bandwidth, but it might save you some headaches.